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A new family of chromatically unique 6-bridge graph. (English) Zbl 1443.05069
Summary: For a graph $$G$$, let $$P(G, \lambda)$$ denote the chromatic polynomial of $$G$$. Two graphs $$G$$ and $$H$$ are chromatically equivalent (or simply $$\chi$$-equivalent), denoted by $$G \sim H$$, if $$P(G, \lambda)=P(H, \lambda)$$. A graph $$G$$ is chromatically unique (or simply $$\chi$$-unique) if for any graph $$H$$ such as $$H \sim G$$, we have $$H \cong G$$, i.e, $$H$$ is isomorphic to $$G$$. In this paper, the chromatic uniqueness of a new family of 6-bridge graph $$\theta (a,a,b,b,b,c)$$ where $$2 \leq a \leq b \leq c$$, is investigated.
##### MSC:
 05C15 Coloring of graphs and hypergraphs 05C31 Graph polynomials
##### Keywords:
chromatic polynomial; chromatically unique; 6-bridge graph
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##### References:
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