On imbalances in multipartite multidigraphs
A k-partite r-digraph(multipartite multidigraph) (or briefly MMD)(k ≥ 3, r ≥ 1) is the result of assigning a direction to each edge of a k-partite multigraph that is without loops and contains at most r edges between any pair of vertices from distinct parts. Let D(X1, X2, ⋯, Xk) be a k-partite r-dig...
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| Format: | EJournal Article |
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GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2018-04-03.
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| LEADER | 02259 am a22002533u 4500 | ||
|---|---|---|---|
| 001 | EJGTA_482_pdf_66 | ||
| 042 | |a dc | ||
| 100 | 1 | 0 | |a Samee, Uma Tul; Department of Mathematics, Islamia College for Science and Commerce, Srinagar, Kashmir, India |e author |
| 100 | 1 | 0 | |e contributor |
| 700 | 1 | 0 | |a Pirzada, Shariefuddin; Department of Mathematics, University of Kashmir, Srinagar, Kashmir, India. |e author |
| 245 | 0 | 0 | |a On imbalances in multipartite multidigraphs |
| 260 | |b GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, |c 2018-04-03. | ||
| 500 | |a https://www.ejgta.org/index.php/ejgta/article/view/482 | ||
| 520 | |a A k-partite r-digraph(multipartite multidigraph) (or briefly MMD)(k ≥ 3, r ≥ 1) is the result of assigning a direction to each edge of a k-partite multigraph that is without loops and contains at most r edges between any pair of vertices from distinct parts. Let D(X1, X2, ⋯, Xk) be a k-partite r-digraph with parts Xi = {xi1, xi2, ⋯, xini}, 1 ≤ i ≤ k. Let dxij + and dxij − be respectively the outdegree and indegree of a vertex xij in Xi. Define axij (or simply aij) as aij = dxij + − dxij − as the imbalance of the vertex xij, 1 ≤ j ≤ ni. In this paper, we characterize the imbalances of k-partite r-digraphs and give a constructive and existence criteria for sequences of integers to be the imbalances of some k-partite r-digraph. Also, we show the existence of a k-partite r-digraph with the given imbalance set. | ||
| 540 | |a Copyright (c) 2018 Electronic Journal of Graph Theory and Applications (EJGTA) | ||
| 546 | |a eng | ||
| 690 | |a digraph, outdegree, imbalance, maximum degree, oriented graph, multipartite multidigraph | ||
| 655 | 7 | |a info:eu-repo/semantics/article |2 local | |
| 655 | 7 | |a info:eu-repo/semantics/publishedVersion |2 local | |
| 655 | 7 | |a Peer-reviewed Article |2 local | |
| 786 | 0 | |n Electronic Journal of Graph Theory and Applications (EJGTA); Vol 6, No 1 (2018): Electronic Journal of Graph Theory and Applications; 84-94 | |
| 786 | 0 | |n 2338-2287 | |
| 787 | 0 | |n https://www.ejgta.org/index.php/ejgta/article/view/482/pdf_66 | |
| 856 | 4 | 1 | |u https://www.ejgta.org/index.php/ejgta/article/view/482/pdf_66 |z Get Fulltext |