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On chromatic uniqueness of uniform subdivisions of graphs

✍ Scribed by C.P. Teo; K.M. Koh

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 492 KB
Volume: 128
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90123-6

No coin nor oath required. For personal study only.

✦ Synopsis

Let u,(G) denote the number of cycles of length k in a graph G. In this paper, we first prove that if G and H are X-equivalent graphs, then ak(G) = a,(H) for all k with g < k < $g -2, where g is the girth of G. This result will then be incorporated with a structural theorem obtained in [7] to show that all uniform subdivisions of some families of graphs, including the complete bipartite graphs and certain cages, are X-unique.

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