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<j≤k. The equitable chromatic number of a graph G, denoted by χ=(G), is the minimum k such that G is equitably k-colorable. The equitable chromatic threshold of a graph G, denoted by χ=*(G), is the minimum t such that G is equitably k-colorable for k<t. The current paper studies equitable chromatic numbers of Kronecker products of graphs. In particular, we give exact values or upper bounds on χ=(G×H) and χ=*(G×H) when G and H are complete graphs, bipartite graphs, paths or cycles.
- Equitable chromatic number
- Equitable chromatic threshold
- Equitable coloring
- Kronecker product