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Chromatic uniqueness of complementary graphs of \(P_{q-1}\). (Chinese. English summary) Zbl 0882.05066
Summary: Let \(P(G,\lambda)\) denote the chromatic polynomial of a graph \(G\). Then \(G\) is said to be chromatically unique if \(P(H,\lambda)= P(G,\lambda)\) implies that \(H\) is isomorphic to \(G\). Let \(P_n\) denote the path with \(n\) vertices, \(\overline G\) denote the complementary graph of \(G\). We prove that \(\overline{P_{q-1}}\) is chromatically unique if \(q>5\) is a prime number.

MSC:
05C15 Coloring of graphs and hypergraphs
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