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Two classes of chromatically unique graphs. (English) Zbl 0697.05027
The chromatic polynomial of a graph G is denoted by P(G;$$\lambda)$$. Then G is said to be chromatically unique if: whenever $$P(H;\lambda)=P(G;\lambda)$$, then the graph H is isomorphic to G. In this paper, two new classes of chromatically unique graphs are presented. One of these is obtained from disjoint $$K_ r$$ (r$$\geq 3)$$ and $$C_ s$$ (s$$\geq 3)$$ by identifying $$e_ 1\in E(K_ r)$$ with $$e_ 2\in C_ s$$. The other is obtained, for $$n\geq r+1\geq 5$$ (with two exceptions corresponding to $$(n,r)=(6,4)$$ and (7,4)), from disjoint $$K_ r$$ and a graph X of order n which is a $$K_ 4$$ homeomorph, by identifying $$K_ 3$$ in $$K_ r$$ with $$K^ 1_ 3$$ in X.
Reviewer: A.T.White

##### MSC:
 05C15 Coloring of graphs and hypergraphs
##### Keywords:
chromatic polynomial; chromatically unique graphs
Full Text:
##### References:
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