Two classes of chromatically unique graphs
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.
scientific article; zbMATH DE number 4142065
scientific article