广义Peterson图的邻点可区别的全染色

The Adjacent Vertex Distinguishing Total Coloring of Extended Petersen Graph

设P_(n,k)是一个简单图,其顶点集和边集分别为:V(P_(n,k))={u_0,u_1,…u_(n-1),v_0,v_1,…v_(n-1)},E(P_(n,k))={u_iu_(i+1),u_iv_i,v_iv_(1+k)},则称P_(n,k)为广义Peterson图,其中n≥5,0<k<n.讨论了当k=1,2时广义Peterson图的邻点可区别的全染色.

Suppose Pn,k is a simple graph, whose vertex set and edge set are V（Pn,k） = V（Pn,k）={u0,u1,…un-1,v0,v1,…vn-1） and E（Pn,k） ={uiui＋1, uivi, vivi＋k} respectively, then Pn,k is called extended Petersen graph, where n ≤5, 0 〈 k 〈 n. When k = 1, 2, the adjacent vertex distinguishing total coloring of extended Petersen graph is discussed in the paper.