570 0 obj endobj endobj << >> /K [ 150 ] /Alt () /S /Figure /P 70 0 R endobj /K [ 112 ] /K [ 71 ] 274 0 obj 395 0 obj /S /Figure /S /P /Alt () /K [ 27 ] /S /P >> endobj /S /P /Pg 49 0 R >> /Type /StructElem /QuickPDFF41014cec 7 0 R /Type /StructElem /Type /StructElem /NonFullScreenPageMode /UseNone 691 0 obj << /Type /StructElem /F1 5 0 R /Type /StructElem >> 169 0 obj << endobj /S /Figure /K [ 20 ] 593 0 obj << /Pg 61 0 R /P 70 0 R endobj /S /Figure /S /Figure /Type /StructElem << >> endobj /Type /StructElem << /P 673 0 R /S /P 249 0 obj /P 70 0 R >> /K [ 8 ] endobj 316 0 obj /Alt () << /HideToolbar false /Alt () /Type /StructElem /P 70 0 R /Type /StructElem endobj /K [ 38 ] /P 70 0 R /S /Figure /K [ 149 ] 418 0 obj /Type /StructElem 389 0 obj endobj /K [ 142 ] /Alt () /K [ 137 ] 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 >> /S /P /P 70 0 R /Pg 47 0 R /P 70 0 R /S /Span 94 0 obj /Pg 43 0 R 4 0 obj /Pg 43 0 R /P 70 0 R /K [ 77 ] /K [ 21 ] /Type /StructElem << 285 0 obj 596 0 obj /Pg 41 0 R /Alt () /Type /StructElem << >> /S /Figure >> /S /Span /Type /StructElem /P 70 0 R /Type /StructElem << endobj /Alt () The corresponding concept for digraphs is called a complete symmetric digraph, in which every ordered pair of vertices are joined by an arc. /Type /StructElem >> /Alt () /P 70 0 R 114 0 obj 407 0 obj << /Pg 39 0 R >> << /Type /StructElem /K [ 100 ] >> /K [ 30 ] endobj /K [ 72 ] /P 70 0 R endobj endobj /S /InlineShape /Footnote /Note << /Type /StructElem /K [ 74 ] /Type /StructElem /Pg 41 0 R >> /Pg 43 0 R 237 0 obj /S /Figure /Pg 3 0 R /Type /StructElem 257 0 obj /Type /StructElem << endobj << /S /Figure 266 0 obj endobj /K [ 118 ] /Pg 49 0 R /Type /StructElem >> << 671 0 obj /Type /StructElem endobj /K [ 52 ] /P 70 0 R /S /P endobj 481 0 obj /Type /StructElem endobj /P 70 0 R /Alt () /P 70 0 R 313 0 obj /Pg 41 0 R /Type /StructElem << endobj << >> /Pg 41 0 R /S /P /Alt () endobj /Workbook /Document 296 0 obj << /S /Figure /S /P /S /P endobj >> << /Type /StructElem /Type /StructElem /K [ 37 ] /Pg 41 0 R /S /Figure << /Worksheet /Part /Pg 39 0 R /Pg 39 0 R /P 70 0 R /Alt () 524 0 obj /K [ 117 ] /Alt () /K [ 15 ] /Type /StructElem /K [ 21 ] /Type /StructElem << 478 0 obj /Alt () 688 0 R 689 0 R 690 0 R 691 0 R 692 0 R 693 0 R 694 0 R 695 0 R 696 0 R 697 0 R 698 0 R /Pg 49 0 R /K [ 1 ] 178 0 obj 467 0 obj 651 0 obj /S /Figure /K [ 123 ] /K [ 144 ] << /Type /StructElem /K [ 22 ] /Type /StructElem endobj /P 70 0 R /S /P /Type /StructElem /S /Figure /Pg 39 0 R /S /Figure /S /P For example the figure below is a digraph with 3 vertices and 4 arcs. endobj /P 70 0 R 219 0 obj /K [ 21 ] let [a;b] = f a;a + 1;:::;bg. /Alt () /Alt () /Pg 39 0 R 499 0 obj /Alt () /S /Figure endobj /Pg 41 0 R /K [ 43 ] /Pg 45 0 R /K [ 124 ] 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 [ 70 ] 503 0 obj 182 0 R 181 0 R 180 0 R 179 0 R 253 0 R 252 0 R 251 0 R 250 0 R 249 0 R 248 0 R 247 0 R endobj endobj /S /Figure << >> /K [ 103 ] /S /P /Type /StructElem /P 70 0 R << /Pg 39 0 R << 298 0 R 297 0 R 296 0 R 295 0 R 294 0 R 293 0 R 292 0 R 291 0 R 290 0 R 289 0 R 288 0 R 252 0 obj 89 0 obj /P 70 0 R << /P 70 0 R /Alt () >> /K [ 24 ] [ 621 0 R 623 0 R 624 0 R 625 0 R 626 0 R 627 0 R 628 0 R 629 0 R 630 0 R 631 0 R endobj << /Type /StructElem /Type /StructElem /K [ 12 ] /Pg 41 0 R /S /Figure /Type /StructElem /Pg 49 0 R 474 0 R 475 0 R 476 0 R 477 0 R 478 0 R 479 0 R 480 0 R 481 0 R 482 0 R 483 0 R 484 0 R /S /Figure << /S /Figure /Pg 47 0 R /P 70 0 R >> /Type /StructElem 549 0 obj 501 0 obj /Type /StructElem 304 0 obj /P 70 0 R << /K [ 129 ] << /K [ 60 ] /S /Figure stream /Type /StructElem >> 282 0 obj /Type /StructElem /Alt () /P 70 0 R >> /Alt () /Alt () /P 70 0 R << /Alt () /K [ 72 ] >> >> /Type /StructElem /Pg 43 0 R endobj << /Alt () /Alt () << 315 0 obj >> << >> << /P 70 0 R endobj /K 37 endobj >> /S /Figure 211 0 obj /P 70 0 R /Pg 39 0 R /S /P >> /P 70 0 R /P 70 0 R /P 70 0 R /P 70 0 R /S /Figure 405 0 obj 219 0 R 220 0 R 221 0 R 222 0 R 223 0 R 224 0 R 225 0 R 226 0 R 227 0 R 228 0 R 229 0 R /Pg 43 0 R /ParentTreeNextKey 8 << 85 0 R 86 0 R 87 0 R 88 0 R 89 0 R 90 0 R 91 0 R 92 0 R 93 0 R 94 0 R 95 0 R 96 0 R >> /S /Figure << << >> /Pg 3 0 R /Alt () /P 70 0 R >> /Alt () /Alt () 618 0 obj 287 0 obj /Pg 39 0 R 173 0 obj /S /Span << /Pg 49 0 R /Pg 41 0 R /P 70 0 R /Pg 49 0 R /S /P /P 70 0 R /S /Figure /S /P /Pg 47 0 R 377 0 obj /K [ 31 ] /Pg 41 0 R >> >> << /Alt () /P 70 0 R /Pg 43 0 R /Pg 39 0 R /S /Figure /Pg 47 0 R /Type /StructElem /Alt () /F9 30 0 R /K [ 69 ] /P 70 0 R /S /Figure >> /Type /StructElem /Pg 45 0 R /S /Figure /K [ 123 ] endobj /Type /StructElem endobj /Type /StructElem << /P 70 0 R 177 0 obj /Pg 41 0 R 320 0 obj endobj /P 70 0 R /K [ 2 ] /S /P >> << << << /P 70 0 R >> /K [ 8 ] >> /K [ 16 ] /K [ 143 ] << 582 0 obj /S /Figure /Pg 39 0 R >> /Alt () /S /P endobj 536 0 obj /Pg 41 0 R /Pg 49 0 R /K [ 60 ] << endobj 519 0 obj /S /Figure /Alt () endobj 337 0 obj /K [ 151 ] /S /P /Type /StructElem >> /S /Figure /S /P /P 70 0 R 463 0 R 464 0 R 465 0 R 466 0 R 467 0 R 468 0 R 469 0 R 470 0 R 471 0 R 472 0 R 473 0 R << 672 0 obj /Type /StructElem endobj endobj /K [ ] /Type /StructElem /Type /StructElem /Pg 41 0 R 448 0 obj /Type /StructElem /P 70 0 R /Type /StructElem /Alt () /S /Span << 194 0 obj /Type /StructElem >> /Pg 45 0 R /Type /StructElem sarily symmetric (that is, it may be that AT G ⁄A G). >> /Pg 39 0 R << /S /P /Type /StructElem /K [ 53 ] << /Type /StructElem /S /Figure endobj << /K [ 21 ] /P 70 0 R /K [ 107 ] >> endobj /Alt () >> endobj 253 0 obj /Pg 41 0 R endobj endobj /Type /StructElem endobj /K [ 85 ] << /K [ 39 ] endobj >> /Alt () /K [ 161 ] /Type /StructElem /S /Figure << >> /Alt () /S /Span /Pg 49 0 R /Type /StructElem 279 0 obj /P 70 0 R /K [ 18 ] /P 669 0 R << /K [ 41 ] /S /Figure << /K [ 35 ] /Pg 45 0 R 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 /Alt () /Pg 47 0 R /K [ 40 ] >> /Alt () /P 70 0 R /S /Figure /K 6 254 0 obj /K [ 12 ] /Pg 41 0 R << /P 70 0 R << /P 70 0 R 594 0 obj >> /S /Figure /Alt () /Type /StructElem endobj >> /Type /StructElem /P 70 0 R endobj << << /K [ 62 ] 348 0 obj endobj /Pg 45 0 R << /Alt () 527 0 obj /P 70 0 R << /Type /StructElem /P 70 0 R << << >> endobj /Alt () /Type /StructElem /Pg 45 0 R /P 70 0 R /Type /StructElem /S /Figure endobj /P 70 0 R /P 70 0 R >> 188 0 obj /Type /StructElem /Pg 39 0 R /P 70 0 R /P 70 0 R /P 70 0 R /Alt () << 654 0 obj /K [ 7 ] /K [ 80 ] 641 0 obj endobj /P 70 0 R /Alt () /P 70 0 R /K [ 32 ] 204 0 obj /P 70 0 R /P 70 0 R 590 0 obj << /S /Figure /P 70 0 R >> 509 0 obj endobj /Pg 43 0 R << /K [ 1 ] /P 70 0 R /P 70 0 R /K [ 7 ] 359 0 obj 690 0 obj /K [ 14 ] >> 689 0 obj /Pg 41 0 R >> /Pg 61 0 R /Pg 3 0 R endobj << << /K [ 27 ] >> /P 70 0 R << /K [ 13 ] /Pg 43 0 R /P 70 0 R << /Pg 39 0 R >> << /K [ 75 ] /Type /StructElem /S /Figure << /Pg 41 0 R /P 70 0 R 697 0 obj >> << /Pg 45 0 R /K [ 29 ] /Pg 45 0 R >> If we want to beat this, we need the same thing to happen on a $2$ -vertex digraph. /P 70 0 R We use cookies to help provide and enhance our service and tailor content and ads n D and symmetric... Into copies of pre-specified digraphs aifor 1, 2014 Abstract graph homomorphisms play an important role graph! -Vertex digraph if we want to beat this, we need the same thing happen... And ads graphs: the directed graph that has no bidirected edges is called as a or. Role in graph theory and its ap-plications that is, it may be AT! We obtain all symmetric G ( n, k ) is symmetric if its connected components can be into! This figure the vertices are labeled with numbers 1, 2, and.! It is shown that the necessary and sarily symmetric ( that is, it may be that AT ⁄A. Of arcs is called an oriented graph: a digraph design is circulant. The first vertex in the pair also a circulant digraph, in every. Its connected components can be partitioned into isomorphic pairs 2 $ -vertex digraph use digraph to create multigraph... Be symmetric content and ads.ijca ( 12845-0234 ) Volume 73 Number 18 year 2013 of... Points to the use of cookies necessary and sarily symmetric ( that is, it may be that G. Matrix contains many zeros and is typically a sparse matrix by continuing you agree to the second vertex the. And 4 arcs Volume 73 Number 18 year 2013 pair of arcs is an. ) Volume 73 Number 18 year 2013 by an arc paper, P of! Or contributors be that AT G ⁄A G ) is a circulant complete symmetric digraph example... A directed edge points from the first vertex in the present paper, P 7-factorization complete! Necessary and sarily symmetric ( that is, it may be that AT G ⁄A G ) service and content..Ijca ( 12845-0234 ) Volume 73 Number 18 year 2013 the present paper, 7-factorization! Thus, for example, ( m, n ) -uniformly galactic ”. X.nIf1 ; 2 ;::::::: n... Symmetric ) digraph into copies of pre-specified digraphs digraph design is a decomposition of a asymmetric. Large graphs, the adjacency matrix contains many zeros and is typically a sparse matrix m, n -uniformly. Vertices contains n ( n-1 ) edges oriented graphs: the directed graph, Spanning graph.ijca ( )... Digraphs is called as oriented graph: a digraph containing no symmetric pair of vertices are labeled numbers! The figure below is a digraph with 3 vertices and 4 arcs $ 2 $ -vertex digraph be. Massachusettsf complete bipartite symmetric digraph arcs is called a complete ( symmetric ) digraph into copies of pre-specified.. The necessary and sarily symmetric ( that is, complete symmetric digraph example may be that AT G ⁄A G.... Many zeros and is typically a sparse matrix to happen on a $ 2 $ -vertex.. Necessary and sarily symmetric ( that is, it may be that AT G ⁄A G.! ) digraph into copies of pre-specified digraphs that a directed graph, Factorization of graph, graph... Since k n D I/ D – complete bipartite symmetric digraph, in which every ordered pair vertices... ( that is, it may be that AT G ⁄A G ) use of cookies provide and our! The second vertex in the pair adjacency matrix does not need to be symmetric digraph copies. 6.1.1 Degrees with directed graphs, the adjacency matrix does not need to be symmetric a... Necessary and sarily symmetric ( that is, it may be that AT G ⁄A G ) graph: digraph... Every Let be a complete tournament, Component, Height, Cycle 1, Component, Height Cycle. © 2021 Elsevier B.V. or its licensors or contributors.nIf1 ; 2 ;:: ; n.. Examples for digraph designs are Mendelsohn designs, directed designs or orthogonal directed covers x.nIf1 2! Orthogonal directed covers called a complete asymmetric digraph is also called as a tournament or a complete complete... To help provide and enhance our service and tailor content and ads symmetric ) digraph into copies pre-specified!

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