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Chromaticity of certain tripartite graphs identified with a path |
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| Authors: | GC Lau YH Peng |
| Institution: | a Faculty of I. T. and Quantitative Science, Universiti Teknologi MARA (Johor Branch), Segamat, Johor, Malaysia b Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Malaysia c Department of Mathematics, Universiti Putra Malaysia, 43400 UPM Serdang, Malaysia |
| Abstract: | 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∪Pm(m?3), (K2,2,2-e)∪Pm(m?5) and (K2,2,2-2e)∪Pm(m?6) by identifying the end-vertices of the path Pm with any two vertices of K2,2,2, K2,2,2-e and K2,2,2-2e, respectively, where e and 2e are, respectively, an edge and any two edges of K2,2,2. As a by-product of this, we obtain some families of chromatically unique and chromatically equivalent classes of graphs. |
| Keywords: | Chromatic polynomial Chromatically unique Chromatically equivalent |
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