×

zbMATH — the first resource for mathematics

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
Keywords:
path; cycle
PDF BibTeX XML Cite