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Two new classes of chromatically unique graphs. (Chinese. English summary) Zbl 1268.05080
Summary: As usual, $$P_n$$ and $$C_n$$ denote the path and cycle of order $$n$$, respectively. Let $$D_n$$ be the graph obtained by identifying a vertex of $$K_3$$ with a 1-degree vertex of $$P_{n-2}$$. In the present article, the coloring of two classes of graphs, $$\overline {(D_{m_1}\cup \cdots \cup D_{m_k})\cup (P_{n_1}\cup \cdots \cup P_{n_t})}$$ and $$\overline {(D_{m_1}\cup \cdots \cup D_{m_k})\cup (C_{n_1}\cup \cdots \cup C_{n_t})}$$, is investigated, and their chromatic uniqueness under certain conditions is proved.

##### MSC:
 05C15 Coloring of graphs and hypergraphs 05C38 Paths and cycles
path; cycle