zbMATH — the first resource for mathematics

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