On imbalances in multipartite multidigraphs
| Main Authors: | Samee, Uma Tul; Department of Mathematics, Islamia College for Science and Commerce, Srinagar, Kashmir, India, Pirzada, Shariefuddin; Department of Mathematics, University of Kashmir, Srinagar, Kashmir, India. |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2018
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| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/482 https://www.ejgta.org/index.php/ejgta/article/view/482/pdf_66 |
Daftar Isi:
- 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.