Equitable colorings of Kronecker products of graphs

Authors:
Wu-Hsiung Lin;Gerard J. Chang
Affiliations:
Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan;Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan and Taida Institute for Mathematical Sciences, National Taiwan University, Taipei 10617, Taiwan and National Center for ...
Venue:
Discrete Applied Mathematics
Year:
2010

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Abstract

For a positive integer k, a graph G is equitably k-colorable if there is a mapping f:V(G)-{1,2,...,k} such that f(x)f(y) whenever xy@?E(G) and ||f^-^1(i)|-|f^-^1(j)||@?1 for 1@?i=t. The current paper studies equitable chromatic numbers of Kronecker products of graphs. In particular, we give exact values or upper bounds on @g"=(GxH) and @g"=^*(GxH) when G and H are complete graphs, bipartite graphs, paths or cycles.