Yang Zhi-lin
Abstract
Let P(G,λ) is the chromatic polynomial of a graph G,and the graph G is chromatically unique if for any graph H,P(H,λ)=P(G,λ) implies H≌G.In this paper,by comparing the numbers of partitions into 4-color classes of the tripartite graphs,it is proved that K(n,n+v,n+k) is chromatically unique for 4≤v+2≤k≤2v and n(k-1)2/4.
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Let P(G,λ) is the chromatic polynomial of a graph G,and the graph G is chromatically unique if for any graph H,P(H,λ)=P(G,λ) implies H≌G.In this paper,by comparing the numbers of partitions into 4-color classes of the tripartite graphs,it is proved that K(n,n+v,n+k) is chromatically unique for 4≤v+2≤k≤2v and n(k-1)2/4.
Key concepts: Combinatorics, Chromatic polynomial, Chromaticity, Mathematics, Graph, Chromatic scale, Discrete mathematics, Friendship graph