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On ?-equivalence and ?-equivalence of graphs

✍ Scribed by Du, Qingyan

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 336 KB
Volume: 21
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199602)21:2<211::aid-jgt11>3.0.co;2-m

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✦ Synopsis

W e define a partial ordering on the set of a-polynomials as well as a vertex splitting operation on the set of graphs, and introduce the notions of (r-equivalence and (r- uniqueness of graphs. Let a ( G ) be the a-polynomial of a graph G and a ( G ) = (r(GC).

Let H = (G, u , A, 5) be a vertex splitting graph of G. We prove that a ( G ) 5 F(H) and the equality holds if and only if every vertex of A is adjacent to every vertex of 5. This gives us an effective means to find v-equivalent and ,y-equivalent graphs. A necessary and sufficient condition for a graph to be X-unique but not (r-unique is also obtained.

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