The chromaticity of the join of tree and null graph L. X. Hung
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ArticleContent type: Текст Media type: электронный Subject(s): хроматическое число | хроматически уникальный граф | хроматический индексGenre/Form: статьи в журналах Online resources: Click here to access online
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Прикладная дискретная математика № 50. С. 93-101Abstract: The chromaticity of the graph G, which is join of the tree Tp and the null graph Oq , is studied. We prove that G is chromatically unique if and only if 1 < p < 3, 1 < q < 2; a graph H and Tp + Op-1 are x-equivalent if and only if H = Tp + Op-1, where Tp is a tree of order p; H and Tp + Op are x-equivalent if and only if H G {Tp + Op, TP+1 + Op-1}, where Tp is a tree of order p, Tp+1 is a tree of order p + 1. We also prove that if p < q, then xz(G) = ch'(G) = A(G); if A(G) = |V(G)| — 1, then x'(G) = ch'(G) = A(G) if and only if G = K3.
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The chromaticity of the graph G, which is join of the tree Tp and the null graph Oq , is studied. We prove that G is chromatically unique if and only if 1 < p < 3, 1 < q < 2; a graph H and Tp + Op-1 are x-equivalent if and only if H = Tp + Op-1, where Tp is a tree of order p; H and Tp + Op are x-equivalent if and only if H G {Tp + Op, TP+1 + Op-1}, where Tp is a tree of order p, Tp+1 is a tree of order p + 1. We also prove that if p < q, then xz(G) = ch'(G) = A(G); if A(G) = |V(G)| — 1, then x'(G) = ch'(G) = A(G) if and only if G = K3.
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