Title of article :
Chromaticity of Complete 6-Partite Graphs with Certain Star or Matching Deleted
Author/Authors :
Roslan, H. Universiti Sains Malaysia - School of Mathematical Sciences, Malaysia , Ameen, A. Sh. Universiti Sains Malaysia - School of Mathematical Sciences, Malaysia , Peng, Y. H. Universiti Putra Malaysia - Institute for Mathematical Research - Department of Mathematics, Malaysia , Zhao, H. X. Qinghai Normal University - Department of Mathematics, China
Abstract :
Let P(G,λ) be the chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically equivalent, denoted G∼H, if P(G,λ)=P(H,λ). We write [G]={H|H∼G}. If [G]={G}, then G is said to be chromatically unique. In this paper, we first characterize certain complete 6-partite graphs with 6n vertices according to the number of 7-independent partitions of G. Using these results, we investigate the chromaticity of G with certain star or matching deleted. As a by-product, many new families of chromatically unique complete 6-partite graphs with certain star or matching deleted are obtained.
Keywords :
Chromatic polynomial , chromatically closed , chromatic uniqueness.
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society
