A(k,r)-coloring of a graph G is a proper k-coloring of graph G such that the neighbors of any vertex receive at least min｛r,d(v)}different colors.The smallest positive integral k such that graph G has a(k,r)-coloring is defined as the r-hued chromatic number and denoted by xr(G).The Cartesian product of two graphs G and H,denoted by G□H,has vertex set V(G)× V(H),where(u1,v1)and(u2,v2)are adjacent if and only if either u1=u2 and v1v2 ∈ E(G),or v1=v2 and u1u2 ∈ E(G).In this paper,the r-hued chromatic number of Wn□Pm is determined.
(k,r)-coloringr-hued chromatic numberCartesian product of graphs
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