On chromatic uniqueness of certain 5-partite graphs |
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Authors: | H Roslan A S Ameen Y H Peng H X Zhao |
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Institution: | 1. School of Mathematical Sciences, University Sains Malaysia, 11800, Penang, Malaysia 2. Department of Mathematics, and Institute for Mathematical Research, University Putra Malaysia, 43400UPM, Serdang, Malaysia 3. Department of Mathematics, Qinghai Normal University, Xining, Qinghai, 810008, China
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Abstract: | Let P(G,λ) be the chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically equivalent, denoted G~H, if P(G,λ)=P(H,λ). We write G]={H∣H~G}. If G]={G}, then G is said to be chromatically unique. In this paper, we first characterize certain complete 5-partite graphs with 5n+3 vertices according to the number of 6-independent partitions of G. Using these results, we investigate the chromaticity of G with certain star or matching deleted. As a by-product, many new families of chromatically unique complete 5-partite graphs with certain star or matching deleted are obtained. |
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