This paper completes the classification of antipodal distance-transitive covers of the complete bipartite graphs K k , k , where k Ρ 3 . For such a cover the antipodal blocks must have size r Ρ k . Although the case r Ο k has already been considered , we give a unified treatment of r Ρ k . We use d
Coverings of complete bipartite graphs and associated structures
β Scribed by John Shawe-Taylor
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 648 KB
- Volume
- 134
- Category
- Article
- ISSN
- 0012-365X
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β¦ Synopsis
A construction is given of distance-regular q-fold covering graphs of the complete bipartite graph K qk,,pk, where q is the power of a prime number and k is any positive integer. Relations with associated distance-biregular graphs are also considered, resulting in the construction of a family of distance-bitransitive graphs.
π SIMILAR VOLUMES
In this paper it is proved that the exponential generating function of the numbers, denoted by N(p, q), of irreducible coverings by edges of the vertices of complete bipartite graphs Kp.q equals exp(xe r + ye x -x -y -xy) -t.
## Abstract A graph is __sβregular__ if its automorphism group acts freely and transitively on the set of __s__βarcs. An infinite family of cubic 1βregular graphs was constructed in [10], as cyclic coverings of the threeβdimensional Hypercube. In this paper, we classify the __s__βregular cyclic cov
## Abstract Given a graph __G__, for each Ο β__V__(__G__) let __L__(Ο ) be a list assignment to __G__. The wellβknown choice number __c__(__G__) is the least integer __j__ such that if |__L__(Ο )| β₯__j__ for all Ο β__V__(__G__), then __G__ has a proper vertex colouring Ο with Ο(Ο ) β __L__ (Ο ) (βΟ β__
## Abstract Let __G__ be a finite graph with directed bipartition (__V__^+^, __V__^β^). Necessary and sufficient conditions are given for the existence of covers and strong covers that: (i) satisfy matching with respect to __V__^+^, and (ii) include a given set of edges that satisfies matching with