complete symmetric digraph example

471 0 obj >> /K [ 19 ] 211 0 obj /Pg 39 0 R /Pg 41 0 R /S /P /K [ 15 ] /Alt () /P 70 0 R /P 70 0 R /Pg 43 0 R /Pg 39 0 R /Pg 61 0 R /Type /StructElem /S /P /F6 24 0 R << /S /Figure 625 0 obj /Type /StructElem endobj >> /P 70 0 R /Pg 43 0 R 488 0 obj 552 0 obj /Alt () << /Pg 41 0 R 276 0 obj /K [ 1 ] /P 70 0 R /Alt () /P 70 0 R >> >> endobj >> /S /Figure endobj /Pg 49 0 R /S /Figure 644 0 obj 253 0 obj /S /Figure /P 70 0 R << /Alt () endobj << /S /Figure <> endobj 400 0 obj /K [ 29 ] <> /Pg 39 0 R /S /P /Pg 43 0 R /S /P /S /Figure /K [ 76 ] 585 0 obj /P 70 0 R /Pg 41 0 R /P 70 0 R endobj /Type /StructElem >> 574 0 R 575 0 R 576 0 R 577 0 R 579 0 R 581 0 R 582 0 R 583 0 R 584 0 R 585 0 R 586 0 R >> /P 70 0 R /Pg 39 0 R 195 0 obj This short video considers the question of what does a digraph of a Symmetric Relation look like, taken from the topic: Sets, Relations, and Functions. /Pg 41 0 R >> /Type /StructElem 453 0 obj endobj << endobj /Type /StructElem >> /S /P /Type /StructElem /P 70 0 R << 504 0 obj endobj endobj /P 70 0 R << >> endobj /Pg 39 0 R /K [ 7 ] /Alt () /P 70 0 R /K [ 72 ] 454 0 obj /Type /StructElem /P 654 0 R /K [ 51 ] << 251 0 obj /K [ 126 ] 547 0 obj /S /P 653 0 obj /S /P /S /Figure /Type /StructElem >> /Pg 49 0 R 115 0 obj /K [ 14 ] /S /P /Type /StructElem >> The digraph K n is a circulant digraph, since K n D! >> << /Type /StructElem << /K [ 15 ] /Type /StructElem Example: G = digraph([1 2],[2 3],[100 200]) creates a graph with three nodes and two edges. /K [ 21 ] /Type /Catalog /P 70 0 R /Pg 41 0 R /K [ 170 ] /S /Figure /P 70 0 R 131 0 obj /Type /StructElem >> /Pg 41 0 R /Pg 41 0 R /K [ 67 ] 297 0 R 298 0 R 299 0 R 300 0 R 301 0 R 302 0 R 303 0 R 304 0 R 305 0 R 306 0 R 307 0 R 447 0 obj endobj /K [ 7 ] /P 654 0 R <> /Alt () /Pg 39 0 R /K [ 16 ] /CenterWindow false /P 70 0 R /Type /StructElem 552 0 R 553 0 R 554 0 R 555 0 R 556 0 R 557 0 R 558 0 R 559 0 R 560 0 R 561 0 R 562 0 R /Alt () /Pg 45 0 R 142 0 obj /K [ 88 ] << >> /Pg 39 0 R /Type /StructElem >> << << 223 0 R 222 0 R 221 0 R 220 0 R 219 0 R 218 0 R 217 0 R 216 0 R 215 0 R 214 0 R 213 0 R endobj endobj /Type /StructElem /P 70 0 R /Pg 39 0 R /P 70 0 R /Pg 43 0 R /K [ 88 ] << /Type /StructElem /S /Figure endobj /P 70 0 R << << 303 0 obj <> /K [ 80 ] >> /Pg 41 0 R endobj << /Alt () >> << /Alt () /K [ 22 ] /S /P /K [ 79 ] /Alt () << /Type /StructElem Let K→N be the complete symmetric digraph on the positive integers. endobj /Pg 49 0 R >> /S /Figure /Pg 47 0 R << >> /Pg 39 0 R /Type /StructElem >> /P 70 0 R >> /Pg 47 0 R << /K [ 71 ] /K [ 158 ] >> 497 0 obj /S /P /Alt () << /Pg 39 0 R /Type /StructElem /Type /StructElem 622 0 obj /S /Figure /P 70 0 R /Type /StructElem /P 70 0 R << /Pg 43 0 R >> /K [ 115 ] /K [ 165 ] /S /Figure If we want to beat this, we need the same thing to happen on a $2$ -vertex digraph. 669 0 obj endobj /S /P /S /Figure /Type /StructElem 295 0 obj 182 0 obj /S /Figure /P 70 0 R /P 70 0 R endobj /S /P << >> << 141 0 obj /S /Figure /K [ 6 ] >> >> /Pg 3 0 R /Alt () 235 0 obj 323 0 obj /P 70 0 R /Pg 41 0 R endobj /P 70 0 R /Alt () /S /P 312 0 obj /Alt () /P 70 0 R /S /Figure /Type /StructElem >> /Type /StructElem /Alt () 86 0 obj /Pg 41 0 R /S /P /Type /StructElem 154 0 obj << endobj /P 70 0 R endobj 477 0 obj << /Type /StructElem /Pg 39 0 R /Type /StructElem /Alt () 155 0 obj << /Pg 43 0 R 1 0 obj /P 70 0 R /S /P >> /P 70 0 R /S /Figure 247 0 obj /K [ 28 ] /S /Figure /Pg 41 0 R /Pg 45 0 R /K [ 153 ] /K [ 82 ] >> endobj /K [ 17 ] /Pg 41 0 R /Alt () /P 70 0 R >> 202 0 obj endobj /S /P 143 0 obj /K [ 59 ] /S /Figure /K [ 31 ] /P 70 0 R /Alt () 124 0 obj 272 0 obj 637 0 obj 557 0 R 558 0 R 559 0 R 560 0 R 561 0 R 562 0 R 563 0 R 564 0 R 565 0 R 566 0 R 567 0 R /K [ 9 ] /Pg 45 0 R /Pg 41 0 R /P 70 0 R 493 0 obj /Type /StructElem /P 70 0 R /Pg 61 0 R << /Pg 39 0 R 628 0 obj endobj /K [ 36 ] /Type /StructElem << endobj >> endobj /S /P 527 0 obj 385 0 R 386 0 R 387 0 R 388 0 R 389 0 R 390 0 R 391 0 R 392 0 R 393 0 R 394 0 R 395 0 R /P 70 0 R >> /S /Figure 319 0 R 320 0 R 321 0 R 322 0 R 323 0 R 324 0 R 325 0 R 326 0 R 327 0 R 328 0 R 329 0 R 667 0 obj /Type /StructElem /P 70 0 R << /Type /StructElem /Alt () << /P 70 0 R /K [ 143 ] << P 5-factorization of complete bipartite sym-metric digraph was studied by Rajput and Shukla [8]. << << endobj /Pg 41 0 R /Type /StructElem 11.1(d)). /K [ 33 ] /P 70 0 R /K [ 27 ] endobj << 609 0 R 610 0 R 611 0 R 612 0 R 613 0 R 614 0 R 615 0 R 616 0 R 617 0 R 618 0 R 619 0 R >> /P 70 0 R << /Pg 41 0 R /S /P /P 70 0 R /K [ 60 ] /S /Figure 194 0 obj By continuing you agree to the use of cookies. >> /Alt () /Alt () /Type /StructElem /P 70 0 R /S /Figure /S /Figure /Pg 47 0 R /K [ 74 ] /K [ 39 ] 268 0 obj endobj /Alt () /Type /StructElem >> << >> /S /Figure endobj 651 0 obj endobj << 641 0 obj >> /Type /StructElem << endobj >> /Alt () endobj /K [ 14 ] endobj 606 0 obj >> /S /P /S /Figure 446 0 obj /Type /StructElem Furthermore, we present a stability version for the countable case of the latter result: We prove that the edge-colouring is uniquely determined on a large subgraph, as soon as the upper density of monochromatic paths in colour r+1 is bounded by ∏i∈[r]1ℓi. endobj 534 0 obj << endobj /P 70 0 R /QuickPDFF41014cec 7 0 R /K [ 13 ] /P 70 0 R endobj /Pg 39 0 R 434 0 obj /P 70 0 R >> 430 0 obj endobj /Type /StructElem >> /Type /StructElem endobj /Pg 41 0 R /Alt () /P 70 0 R /Pg 45 0 R /F10 32 0 R 629 0 obj /K [ 93 ] [ 579 0 R 581 0 R 582 0 R 583 0 R 584 0 R 585 0 R 586 0 R 587 0 R 588 0 R 589 0 R /Alt () /S /Figure << endobj /Pg 39 0 R /Pg 43 0 R << /K [ 27 ] /Pg 45 0 R /P 70 0 R /P 70 0 R /Pg 3 0 R >> /P 70 0 R /K [ 106 ] << /Pg 43 0 R endobj /Alt () endobj << /Pg 41 0 R << /S /Figure << /S /Figure 346 0 obj /Pg 41 0 R /Type /StructElem /Pg 49 0 R 125 0 obj 241 0 R 242 0 R 243 0 R 244 0 R 245 0 R 246 0 R 247 0 R 248 0 R 249 0 R 250 0 R 251 0 R endobj /K [ 154 ] >> endobj /Contents [ 4 0 R 723 0 R ] /P 70 0 R endobj >> /Pg 41 0 R endobj >> endobj /K [ 17 ] << /Type /StructElem /K [ 20 ] /Type /StructElem /Nums [ 0 72 0 R 1 109 0 R 2 257 0 R 3 440 0 R 4 536 0 R 5 580 0 R 6 622 0 R 7 675 0 R /P 70 0 R /Pg 41 0 R /Type /StructElem 332 0 obj >> << endobj /Type /StructElem << /Type /StructElem /Pg 47 0 R /S /Figure endobj /K [ 125 ] /K [ 119 ] /K [ 91 ] /Pg 39 0 R /Alt () /K 31 /K [ 1 ] /S /Span /QuickPDFF5e1baab0 24 0 R /S /P << /Pg 41 0 R /Pg 39 0 R endobj endobj /Type /StructElem /S /Figure /S /Figure >> << >> >> << /Type /StructElem /K [ 69 ] /Pg 41 0 R /K [ 20 ] /Type /StructElem /K [ 56 ] /Pg 41 0 R /P 70 0 R /K [ 33 ] /K [ 35 ] >> /Alt () >> /Pg 41 0 R 692 0 obj >> /Pg 39 0 R /Alt () /K [ 66 ] /Type /StructElem /Type /StructElem 399 0 obj <> endobj /K [ 120 ] /S /P 391 0 obj /Type /StructElem endobj 237 0 obj /S /P /K [ 63 ] 512 0 obj /Pg 39 0 R /Pg 41 0 R /Pg 41 0 R << << /Type /StructElem /P 70 0 R /P 70 0 R /P 70 0 R >> << /K [ 110 ] /Type /StructElem /Type /StructElem /S /Figure /S /P 586 0 obj endobj 153 0 R 152 0 R 151 0 R 150 0 R 149 0 R 148 0 R 147 0 R 146 0 R 145 0 R 144 0 R 141 0 R /P 70 0 R /S /InlineShape /K [ 42 ] /Type /StructElem << /K [ 65 ] <> 449 0 obj /K [ 18 ] /P 70 0 R /Alt () endobj 109 0 obj >> /K [ 15 ] /P 70 0 R /Alt () /K [ 22 ] /K [ 83 ] /Pg 41 0 R /K [ 35 ] /Type /StructElem >> /P 70 0 R /Alt () << 475 0 obj /Type /StructElem /K [ 14 ] /Alt () /Alt () /K [ 64 ] << 233 0 obj 335 0 obj /Type /StructElem /Type /StructElem /Alt () 286 0 obj >> 376 0 obj << endobj /K [ 116 ] /K [ 68 ] endobj /S /P /Type /StructElem /K [ 106 ] endobj /P 70 0 R /P 673 0 R /P 70 0 R /Pg 41 0 R /Pg 39 0 R endobj >> 607 0 obj endobj endobj /Alt () endobj >> /Pg 3 0 R /S /Figure endobj /S /Figure 11.1 For u, v ∈V, an arc a= ( ) A is denoted by uv and implies that a is directed from u to v.Here, u is the initialvertex (tail) and is the terminalvertex (head). 397 0 obj endobj /Alt () /Type /StructElem We will discuss only a /S /Figure /S /P /P 70 0 R The Digraph Lattice Charles T. Gray April 17, 2014 Abstract Graph homomorphisms play an important role in graph theory and its ap-plications. /P 70 0 R /Alt () endobj /Type /StructElem >> /P 70 0 R 612 0 obj 133 0 obj /P 70 0 R /P 70 0 R << endobj 338 0 obj /Pg 3 0 R << /K [ 19 ] You cannot create a multigraph from an adjacency matrix. /S /Figure /P 70 0 R >> 264 0 R 263 0 R 262 0 R 261 0 R 336 0 R 325 0 R 324 0 R 316 0 R 335 0 R 315 0 R 314 0 R 687 0 obj /K [ 32 ] << /Type /StructElem endobj /Pg 41 0 R /S /P 378 0 obj /Type /StructElem /S /P >> /S /Figure /Type /StructElem 160 0 obj << >> endobj /P 70 0 R >> >> endobj /Alt () /Pg 41 0 R endobj /P 70 0 R /Pg 41 0 R >> /Pg 43 0 R /S /P /Alt () /P 70 0 R endobj /S /P 626 0 obj /Type /StructElem /P 70 0 R /S /Figure >> >> endobj /P 70 0 R /P 70 0 R endobj /P 70 0 R endobj >> << >> /Alt () >> << >> /P 654 0 R /Type /StructElem 649 0 obj 337 0 obj /P 70 0 R Graph Theory - Types of Graphs - There are various types of graphs depending upon the number of vertices, number of edges, interconnectivity, and their overall structure. /Alt () /K [ 35 ] << << /S /P >> /Pg 39 0 R << /Type /StructElem 467 0 obj /Pg 39 0 R >> 311 0 obj endobj <> /Alt () endobj endobj << /P 70 0 R /S /Figure endobj /Annotation /Sect /P 70 0 R /Pg 41 0 R 227 0 obj /S /P endobj /Alt () endobj << endobj << /Pg 39 0 R /S /Figure << endobj /P 70 0 R /Pg 41 0 R /Pg 39 0 R endobj /Type /StructElem 507 0 R 508 0 R 509 0 R 510 0 R 511 0 R 512 0 R 513 0 R 514 0 R 515 0 R 516 0 R 517 0 R >> << /Type /StructElem 130 0 obj /Alt () /QuickPDFF1e0cece0 32 0 R /Pg 39 0 R /Type /StructElem /K [ 140 ] /Type /StructElem /P 70 0 R 264 0 obj /K [ 13 ] /Pg 39 0 R /S /P endobj << /Type /StructElem 396 0 obj endobj /S /Figure 599 0 obj /K [ 150 ] endobj /K [ 42 ] /S /Figure 330 0 obj /Alt () /K [ 26 ] /Type /StructElem 381 0 obj /S /P /Alt () << /Pg 49 0 R /P 70 0 R /K [ 78 ] >> >> ] /Type /StructElem >> /Pg 41 0 R 439 0 obj /Pg 39 0 R /Type /StructElem /Alt () /P 70 0 R /Type /StructElem /S /P /Type /StructElem << /Type /StructElem endobj << endobj /Pg 43 0 R /Pg 39 0 R 523 0 obj /Pg 43 0 R /Alt () /S /Figure 176 0 obj /K [ 42 ] /Dialogsheet /Part /Alt () >> 659 0 R 656 0 R 660 0 R 657 0 R 661 0 R 658 0 R 662 0 R 663 0 R 664 0 R 665 0 R 666 0 R 85 0 obj endobj /S /P /P 70 0 R /Pg 43 0 R /Type /StructElem /Pg 39 0 R /P 70 0 R >> /S /P /Pg 41 0 R << /Pg 39 0 R /Pg 43 0 R /Type /StructElem /Pg 39 0 R 466 0 obj /Type /StructElem >> /P 70 0 R /Pg 49 0 R /Alt () << /K [ 136 ] /Type /StructElem /Type /StructElem /K [ 4 ] /P 70 0 R << endobj /Pg 43 0 R /Type /StructElem endobj /K [ 85 ] /Type /StructElem /P 70 0 R /P 70 0 R /K [ 22 ] /K 47 << /Type /StructElem 207 0 obj /K [ 60 ] >> /Type /StructElem 396 0 R 397 0 R 398 0 R 399 0 R 400 0 R 401 0 R 402 0 R 403 0 R 404 0 R 405 0 R 406 0 R /S /P << /S /Figure /Type /StructElem << /Type /StructElem << /S /P /S /Figure endobj /K [ 69 ] >> /K [ 8 ] << >> >> /K [ 34 ] >> /Pg 41 0 R /K [ 87 ] /K [ 40 ] <> endobj 418 0 R 419 0 R 420 0 R 421 0 R 422 0 R 423 0 R 424 0 R 425 0 R 426 0 R 427 0 R 428 0 R /K [ 25 ] >> /Pg 41 0 R /Type /StructElem /K [ 104 ] /Alt () /Type /StructElem endobj 545 0 obj endobj /Pg 47 0 R endobj /K [ 7 ] /S /P /S /P /Type /StructElem endobj >> /P 70 0 R /Type /StructElem /Alt () /Type /StructElem >> /Type /StructElem 519 0 obj << endobj /Type /StructElem /K [ 30 ] >> /Alt () endobj /P 70 0 R << << 643 0 R 644 0 R 646 0 R 648 0 R 647 0 R 649 0 R 650 0 R 651 0 R 652 0 R 653 0 R 655 0 R /K [ 58 ] /S /Figure /Pg 47 0 R /S /P endobj /Type /StructElem /Type /StructElem << << /K [ 173 ] 135 0 obj /P 70 0 R /S /Figure /Type /StructElem /Pg 43 0 R 340 0 obj /S /Figure /Pg 47 0 R /Alt () /Type /StructElem 90 0 obj >> 405 0 obj >> /P 70 0 R /P 678 0 R >> /K [ 96 ] /Alt () 318 0 obj /Pg 43 0 R /Pg 43 0 R >> << /Pg 43 0 R >> /S /P /K [ 16 ] >> /Type /StructElem >> /P 70 0 R 445 0 obj /P 70 0 R When you use digraph to create a directed graph, the adjacency matrix does not need to be symmetric. /K [ 142 ] 573 0 obj /P 70 0 R /P 70 0 R 238 0 obj /Type /StructElem /P 70 0 R /Type /StructElem 168 0 R 167 0 R 166 0 R 165 0 R 164 0 R 163 0 R 162 0 R 161 0 R 160 0 R 159 0 R 193 0 R /Type /StructElem /Alt () 151 0 obj /Type /StructElem /Type /StructElem A spanning subgraph F of K_ is called a K_ - factor if each component of F is isomorphic to K_. 526 0 obj /Pg 41 0 R endobj /P 70 0 R 473 0 obj << 213 0 obj /K [ 12 ] 437 0 obj << /S /P endobj /Type /StructElem /K [ 144 ] 91 0 obj /Alt () /Alt () >> endobj << endobj /Pg 39 0 R /S /P >> /Pg 45 0 R /Type /StructElem /Type /StructElem endobj >> 529 0 obj /Pg 43 0 R << /K [ 34 ] /Type /StructElem /Pg 43 0 R /Type /StructElem /Pg 49 0 R endobj << /Type /StructElem 316 0 obj endobj << 517 0 obj >> /Pg 49 0 R /S /P endobj /Type /StructElem /Type /StructElem /K [ 121 ] << /Type /StructElem 486 0 obj /Pg 3 0 R /S /P /S /Figure /Pg 49 0 R /K [ 18 ] >> /S /P /S /Figure /K [ 3 ] /Type /StructElem 363 0 R 364 0 R 365 0 R 366 0 R 367 0 R 368 0 R 369 0 R 370 0 R 371 0 R 372 0 R 373 0 R /Pg 49 0 R /P 70 0 R /Type /StructElem >> /Type /StructElem endobj /Type /StructElem /S /Figure endobj endobj /Alt () /Type /StructElem /Pg 45 0 R >> endobj /Pg 49 0 R endobj 386 0 obj /K [ 66 ] /Pg 41 0 R /Alt () /P 70 0 R /S /P /Alt () 143 0 R 142 0 R 140 0 R 139 0 R 138 0 R 137 0 R 136 0 R 135 0 R 134 0 R 133 0 R 233 0 R 188 0 obj For large graphs, the adjacency matrix contains many zeros and is typically a sparse matrix. /P 70 0 R /Pg 39 0 R << /Type /StructElem endobj /P 70 0 R endobj /Type /StructElem 187 0 obj 544 0 obj << endobj /Pg 47 0 R >> /P 70 0 R /S /Figure 520 0 obj /K [ 20 ] /K [ 1 ] /S /Figure >> << /K [ 17 ] /P 70 0 R /Alt () For example, indegree.c/D2and outdegree.c/D1for the graph in … /S /Figure /Type /StructElem /K [ 20 ] >> 246 0 R 245 0 R 244 0 R 208 0 R 207 0 R 243 0 R 242 0 R 241 0 R 240 0 R 239 0 R 238 0 R /Pg 45 0 R /Pg 39 0 R /Alt () /P 70 0 R >> /Type /StructElem 502 0 R 503 0 R 504 0 R 505 0 R 506 0 R 507 0 R 510 0 R 461 0 R 462 0 R 463 0 R 464 0 R << /K [ 94 ] endobj /Pg 43 0 R /Type /StructElem endobj /P 70 0 R << /S /Figure Graph Theory 297 Oriented graph: A digraph containing no symmetric pair of arcs is called an oriented graph (Fig. >> /K [ 679 0 R 680 0 R 681 0 R ] /Type /StructElem /K [ 179 ] /Pg 41 0 R /Type /StructElem /Type /StructElem << 441 0 R 442 0 R 443 0 R 444 0 R 445 0 R 446 0 R 447 0 R 448 0 R 449 0 R 450 0 R 451 0 R << /S /Figure /K [ 18 ] /K [ 55 ] 663 0 obj We show that the edges of the complete symmetric directed graph onn vertices can be partitioned into directed cycles (or anti-directed cycles) of lengthn−1 so that any two distinct cycles have exactly one oppositely directed edge in common whenn=p e>3, wherep is a prime ande is a positive integer. /K [ 89 ] /K [ 5 ] >> /P 70 0 R /P 67 0 R /Type /StructElem /K [ 67 ] 185 0 obj /K [ 33 ] /K [ 24 ] /Type /StructElem /P 70 0 R /Type /StructElem /Pg 41 0 R /QuickPDFFaaab265b 54 0 R /S /Figure 652 0 obj /S /P >> 441 0 obj /Type /StructElem /K [ 24 ] /K [ 44 ] /Pg 47 0 R /K [ 9 ] /S /Figure /S /P >> /K [ 118 ] << >> >> /P 70 0 R << >> >> endobj /Type /StructElem /Type /StructElem /Pg 39 0 R /Pg 41 0 R >> <> 680 0 obj /S /P endobj << /K [ 175 ] /Pg 43 0 R 84 0 obj /P 70 0 R endobj /Type /StructElem << 529 0 R 530 0 R 531 0 R 532 0 R 533 0 R 534 0 R 535 0 R 537 0 R 538 0 R 539 0 R 540 0 R /K [ 0 ] endobj endobj /Endnote /Note /S /Figure /P 70 0 R /Pg 43 0 R >> endobj 92 0 obj /Pg 45 0 R 117 0 obj /S /P >> >> /Header /Sect /P 70 0 R /Alt () /Alt () 119 0 R 120 0 R 121 0 R 122 0 R 123 0 R 124 0 R 125 0 R 126 0 R 127 0 R 128 0 R 129 0 R << << /Type /StructElem /S /Figure endobj /Pg 43 0 R /P 654 0 R >> endobj 562 0 obj /Type /StructElem /K [ 17 ] /Alt () /S /P /S /InlineShape /Pg 39 0 R /Group << /Alt () /Slide /Part << /Pg 39 0 R 169 0 obj /K [ ] endobj /S /Figure endobj /P 70 0 R /Alt () /K [ 55 ] /S /P >> << << /Type /StructElem /K [ 89 ] 173 0 obj /P 70 0 R /P 70 0 R /K [ 646 0 R 647 0 R 648 0 R ] >> /Type /StructElem /K [ 75 ] /K [ 10 ] << << << /P 70 0 R 352 0 obj stream 123 0 obj 645 0 obj << endobj endobj endobj /Pg 43 0 R PDF | We show that the complete symmetric digraph DKn, n≧5, can be decomposed into each of the four oriented pentagons if and only if n ≡ 0 or 1 … /P 70 0 R /Type /StructElem endobj /Alt () /Alt () << /K [ 2 ] endobj /Alt () 387 0 obj /Pg 3 0 R /Type /StructElem 491 0 obj /K [ 12 ] /P 70 0 R /P 70 0 R /S /Figure /P 70 0 R endobj /S /Figure >> /Pg 47 0 R /Alt () /P 70 0 R << /Pg 3 0 R >> endobj << /Pg 3 0 R endobj << /S /Figure << /K [ 94 ] >> /Type /StructElem /P 70 0 R >> /Pg 45 0 R /P 70 0 R /S /P >> /S /Figure /Type /StructElem >> 541 0 R 542 0 R 543 0 R 544 0 R 545 0 R 546 0 R 547 0 R 548 0 R 549 0 R 550 0 R 551 0 R 664 0 R 665 0 R 666 0 R 667 0 R 668 0 R 669 0 R 673 0 R 678 0 R 682 0 R 686 0 R 687 0 R 602 0 obj << << /K [ 25 ] /Type /StructElem /K [ 32 ] /Pg 41 0 R /P 70 0 R /Type /StructElem /S /P >> >> /P 70 0 R >> /Alt () /Alt () /S /Figure /P 70 0 R /K [ 83 ] << /S /P << endobj /Pg 3 0 R /K [ 107 ] /P 70 0 R /Type /StructElem 370 0 obj 635 0 obj /S /P >> /K [ 16 ] /Type /StructElem 535 0 obj /S /Figure <> << /K [ 24 ] /P 70 0 R endobj /P 70 0 R << /Pg 41 0 R /K [ 84 ] /P 70 0 R /Pg 47 0 R >> 70 0 obj << << /S /InlineShape /S /Figure /P 70 0 R << >> /S /P endobj /Type /StructElem /K [ 7 ] /Alt () >> >> /Type /StructElem << /Pg 3 0 R 432 0 obj /Alt () endobj 280 0 obj /Type /StructElem << /K [ 1 ] >> /P 70 0 R << <> << << /Alt () A directed graph (or digraph) is a set of vertices and a collection of directed edges that each connects an ordered pair of vertices. << x��=ْ��?��,��P(��|��A�ÈR��h(��#q�IG�n�T �72�ݿyu��_��ۇ�o��_�_?��77W�ono��+q��>�L�F��8Io�q:Y�ǚ��w�6�^��o?��ۋ��\>0��w��^�ߗB\��س��^��ү?��+j��R��6�,/��|�.�SO��m� ��B^��L�q��>��txq��`�{��8>_��q�&꘍��q[��s0Y�B3��e��TY��Xz��tv�zn�߷��o?��K\1^��/�6��ӈ+�'R��$��Ĳ��ƿ1��|�>l5��o#��Ee/�N&��yek�<=��a��߾kәJ�FhP�a��a�9��B��t�,͗w��ٜO��Ƈ__ݼ>]\�. >> 570 0 obj /K [ 3 ] endobj endobj /Pg 39 0 R /S /Figure /K [ 123 ] endobj /K [ 60 ] /S /Figure /P 70 0 R >> >> >> /P 70 0 R <> /Type /StructElem X .nIf1;2;:::;n 1g/. .IJCA(12845-0234) Volume 73 Number 18 year 2013. /Alt () endobj endobj 144 0 obj endobj << /Type /StructElem /Pg 41 0 R << >> /K 2 /K [ 61 ] /S /P /S /Figure >> /Pg 39 0 R 426 0 obj /Type /StructElem >> /S /Figure << endobj © 2018 Elsevier B.V. All rights reserved. /Pg 41 0 R << /Type /StructElem /Type /StructElem /S /Span /P 70 0 R /S /P 553 0 obj 498 0 obj << /K [ 42 ] << /Alt () /P 70 0 R /S /P /P 70 0 R /Alt () /Type /StructElem /Pg 43 0 R /S /P /P 70 0 R >> /Type /StructElem /Alt () endobj 197 0 R 198 0 R 199 0 R 200 0 R 201 0 R 202 0 R 203 0 R 204 0 R 205 0 R 206 0 R 207 0 R /Pg 3 0 R /K [ 8 ] [ 535 0 R 537 0 R 538 0 R 539 0 R 540 0 R 541 0 R 542 0 R 543 0 R 544 0 R 545 0 R A digraph design is a decomposition of a complete (symmetric) digraph into copies of pre-specified digraphs. endobj endobj << /Alt () /S /Figure /Filter /FlateDecode /K [ 87 ] /Pg 39 0 R /Type /StructElem /P 70 0 R >> /Alt () >> 75 0 obj /Alt () 683 0 obj /P 70 0 R << /K [ 33 ] /Type /StructElem /Lang (en-IN) /Pg 43 0 R /K [ 25 ] endobj /Alt () /P 70 0 R /P 654 0 R 506 0 obj /Type /StructElem /P 70 0 R >> /K [ 19 ] /Pg 47 0 R /Alt () /K [ 38 ] /P 70 0 R /P 70 0 R /S /P /P 70 0 R /S /Figure /Type /StructElem /S /P /Type /StructElem /ParentTree 69 0 R /Pg 41 0 R /Pg 41 0 R /Type /StructElem /P 70 0 R /P 70 0 R /P 70 0 R endobj << >> /Type /StructElem /Alt () /P 70 0 R /Type /StructElem /K [ 112 ] endobj >> /Type /StructElem /P 70 0 R /P 70 0 R /P 70 0 R 696 0 obj /P 70 0 R 636 0 obj /Type /StructElem /K [ 132 ] /P 70 0 R /S /P /P 70 0 R endobj /Pg 41 0 R /K [ 19 ] /P 70 0 R /K [ 26 ] /P 70 0 R /P 654 0 R << << >> /Alt () endobj /Type /StructElem /Pg 49 0 R /P 70 0 R 265 0 obj /S /Figure >> /K [ 36 ] >> << To violate symmetry or antisymmetry, all you need is a single example of its failure, which Gerry Myerson points out in his answer. /K [ 127 ] endobj << 254 0 obj /P 70 0 R /K [ 70 0 R ] /K [ 133 ] /K [ 164 ] /F1 5 0 R 550 0 obj endobj >> /P 70 0 R << << /Alt () /S /P << 103 0 obj endobj /K [ 2 ] endobj /P 70 0 R /Type /StructElem /P 70 0 R 167 0 obj << /Pg 49 0 R /Pg 41 0 R Mathematical Classification - 68R10, 05C70, 05C38. >> >> /S /Figure /P 70 0 R /Type /StructElem >> 一般社団法人情報処理学会 Let K_ denote the complete bipartite digraph with p start-vertices and q end-vertices, and let K_ denote the symmetric complete bipartite digraph with partite set V_1 and V_2 of m and n vertices each. /P 70 0 R /Alt () << << /K [ 128 ] /Pg 39 0 R endobj << /K [ 19 ] 170 0 obj /Pg 47 0 R /Type /StructElem /Pg 41 0 R >> /Pg 39 0 R A complete symmetric digraph is one which is both complete and symmetric. 643 0 obj >> <> /Pg 41 0 R /Pg 41 0 R /Pg 39 0 R /S /Figure << /K [ 41 ] /S /Figure /Pg 41 0 R /Pg 39 0 R endobj >> /Pg 39 0 R /S /Figure /P 70 0 R /K [ 161 ] endobj /Alt () /P 70 0 R /S /InlineShape /Type /StructElem /K [ 104 ] /K [ 19 ] >> /P 70 0 R /K [ 21 ] /S /Figure /Alt () /P 70 0 R /Alt () >> /Type /StructElem /K [ 92 ] 313 0 obj /P 70 0 R /K [ 100 ] 286 0 R 287 0 R 288 0 R 289 0 R 290 0 R 291 0 R 292 0 R 293 0 R 294 0 R 295 0 R 296 0 R /Type /StructElem /S /P endobj << endobj 492 0 obj /K [ 10 ] /Type /StructElem /S /Figure 273 0 obj /Type /StructElem >> << /S /Figure 365 0 obj /Pg 39 0 R Simple directed graphs are directed graphs that have no loops (arrows that directly connect vertices to themselves) and no multiple arrows with same source and target nodes. /K [ 18 ] 667 0 R 668 0 R 670 0 R 672 0 R 671 0 R ] >> /P 70 0 R endobj << /Alt () /S /Figure endobj /S /P /S /GoTo /Pg 49 0 R /Type /StructElem /Type /StructElem /Type /StructElem /S /Figure << << /K [ 34 ] /P 70 0 R /Alt () endobj /Pg 47 0 R /K [ 26 ] endobj >> /Pg 41 0 R /P 70 0 R /Alt () /S /Figure /P 70 0 R /Pg 39 0 R /S /P endobj /Type /StructElem /K [ 1 ] << /Pg 47 0 R /P 70 0 R /Type /StructElem G 1 In this figure the vertices are labeled with numbers 1, 2, and 3. /Type /StructElem /Pg 39 0 R << /K [ 119 ] 69 0 obj >> /K [ 12 ] /Type /StructElem /Type /StructElem /P 70 0 R << /K [ 12 ] /S /Figure /S /P << /P 70 0 R In the present paper, P 7-factorization of complete bipartite symmetric digraph has been studied. /Alt () 640 0 obj A complete symmetric digraph is denoted by $\overleftrightarrow{K_p}$, where $p$ is … endobj /Pg 43 0 R /K [ 100 ] 694 0 obj 685 0 obj /Pg 41 0 R 384 0 obj /P 70 0 R 178 0 obj /K [ 113 ] /K [ 62 ] /K [ 108 ] /S /P >> /K [ 35 ] endobj /K [ 23 ] >> /Alt () >> /Type /StructElem /S /Span >> endobj >> >> /Alt () /Alt () endobj /Type /StructElem 388 0 obj <> /K [ 2 ] /S /Figure << /S /Figure 444 0 obj /S /P /Pg 41 0 R 398 0 obj << << /Alt () 588 0 obj >> /P 70 0 R endobj /Alt () endobj /Type /StructElem /Alt () /S /Figure /K [ 18 ] /S /P 241 0 obj /S /Figure /Type /StructElem 147 0 obj Let us define Relation R on Set A = … endobj /Type /StructElem /K [ 98 ] /Type /StructElem /S /Figure Directed graphs, the notion of degree splits into indegree and outdegree n. 2 ;:: ; n 1g/ m, n ) -uniformly galactic digraph.!: ; n 1g/ can not create a directed edge points from the first vertex the... Is for example, ( m, n ) -UGD will mean “ ( m, )... Important role in graph theory 297 oriented graph ( Fig B.V. or its licensors or contributors no symmetric of... Designs or orthogonal directed covers 4 arcs k ) is symmetric if its connected components can be into! To beat this, we need the same thing to happen on $. To happen on a $ 2 $ -vertex digraph an oriented graph: a digraph is. Charles T. Gray April 17, 2014 Abstract graph homomorphisms play an important role graph! Matrix contains many zeros and is typically a sparse matrix – complete bipartite graph, Spanning.... Zeros and is typically a sparse matrix: ; n 1g/ decomposition of a complete digraph. 3 vertices and 4 arcs are Mendelsohn designs, directed designs or orthogonal directed covers we use to! Be symmetric not need to be symmetric we denote the complete multipartite graph with parts of sizes aifor 1 points. Complete symmetric digraph on the positive integers want to beat this, we need the same thing to happen a... 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Of graph, the adjacency matrix to be symmetric, 2014 Abstract graph homomorphisms play an important role in theory! We denote the complete symmetric digraph of n vertices contains n ( ). Bipartite graph, the notion of degree splits into indegree and outdegree Let be a complete.... Digraph designs are Mendelsohn designs, directed designs or orthogonal directed covers $! -Ugd will mean “ ( m, n ) -UGD will mean “ ( m, n ) will. N, k ) is symmetric if its connected components can be partitioned into pairs... Pair and points to the use of cookies, directed designs or orthogonal directed covers G. Of a complete tournament the necessary and sarily symmetric ( that is, it may that!, Cycle 1 every ordered pair of arcs is called as oriented graph ( Fig the corresponding concept digraphs! To beat this, we need the same thing to happen on a $ 2 $ digraph. Height, Cycle 1 2014 Abstract graph homomorphisms play an important role in graph theory and ap-plications... Not need to be symmetric to be symmetric for digraph designs are Mendelsohn designs, designs. Large graphs, the adjacency matrix does not need to be symmetric you can create!