Chromatic uniqueness of certain tripartite graphs identified with a path / G.C. Lau and Y.H. Peng
For a graph G, let P (G) be its chromatic polynomial. Two graphs G and H are chromatically equivalent if P(G) = P(H). A graph G is chromatically unique if P(H) = P(G) implies that H == G. In this paper, we classify the chromatic classes of graphs obtained from K2,2,2 u Pm (m ≥ 3) (respectively, (K2,...
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2004.
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| Summary: | For a graph G, let P (G) be its chromatic polynomial. Two graphs G and H are chromatically equivalent if P(G) = P(H). A graph G is chromatically unique if P(H) = P(G) implies that H == G. In this paper, we classify the chromatic classes of graphs obtained from K2,2,2 u Pm (m ≥ 3) (respectively, (K2,2,2 - e) u Pm (m ≥ 5) where e is an edge of K2,2,2) by identifying the end vertices of the path Pm with any two vertices of K2,2,2 (respectively, K2,2,2 - e). As a by-product of this; we obtained some families of chromatically unique and chromatically equivalent classes of graphs. |
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| Item Description: | https://ir.uitm.edu.my/id/eprint/50424/1/50424.PDF |