| Autor: |
Zhi-Yi Guo, Chong-Yun Chao, Nian-Zu Li |
| Rok vydání: |
1997 |
| Předmět: |
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| Zdroj: |
Discrete Mathematics. 172(1-3):9-16 |
| ISSN: |
0012-365X |
| DOI: |
10.1016/s0012-365x(96)00263-4 |
| Popis: |
Let q be a positive integer. A graph G is said to be a q-graph if it contains a q-tree as one of its spanning subgraphs. A connected graph is a 1-graph. (1) We prove that if G is a q-graph with |V(G)| > q, then the multiplicity of the root q of the chromatic polynomial P(G, λ) is the number of q-blocks (maximal subgraphs without any separating Kq in G). This is a generalization of a result in Whitehead and Zhao (1984). (2) We give a characterization of G being chromatically unique. This is a generalization of a result in Chia (1986). (3) Let q ⩽ m and Km(q) be the graph obtained by joining q edges between a complete graph Km with m vertices and a vertex. We show that Km(q) is chromatically unique. This is a generalization of a result in Giudici (1985). |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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