We show that a necessary and sufficient condition for the existence of an \(\bar{S}_{2 q+1}\) - factorization of the symmetric complete tripartite multi-digraph \(\lambda K_{n_{1}, n_{2}, n_{3}}^{*}\) is (i) \(n_{1}=n_{2}=n_{3}\) for \(q=1\) and (ii) \(n_{1}=n_{2}=n_{3} \equiv 0(\bmod (2 q+1) q / d)
Star-factorization of symmetric complete bipartite digraphs
โ Scribed by Kazuhiko Ushio
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 174 KB
- Volume
- 167-168
- Category
- Article
- ISSN
- 0012-365X
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โฆ Synopsis
We show that a necessary and sufficient condition for the existence of an Sk-factorization of the symmetric complete bipartite digraph K*, is m = n -~ 0 (mod k(k -1)).
๐ SIMILAR VOLUMES
In the context of the degree/diameter problem for directed graphs, it is known that the number of vertices of a strongly connected bipartite digraph satisfies a Moore-like bound in terms of its diameter k and the maximum outdegrees (d 1 , d 2 ) of its partite sets of vertices. In this work, we defi
P,-factorization of K,,,, is (i) m + n -0 (mod 3), (ii) m < 2n, (iii) n s 2m and (iv) 3mn/2(m + n) is an integer.
We conclude the study of complete K1,q-factorizations of complete bipartite graphs of the form Kn,n and show that, so long as the obvious Basic Arithmetic Conditions are satisfied, such complete factorizations must exist.
## Abstract Let __Z__~__p__~ denote the cyclic group of order __p__ where __p__ is a prime number. Let __X__ = __X__(__Z__~__p__~, __H__) denote the Cayley digraph of __Z__~__p__~ with respect to the symbol __H__. We obtain a necessary and sufficient condition on __H__ so that the complete graph on