ADJACENT VERTEX DISTINGUISHING TOTAL COLORING OF Pn AND Cn DOUBLE GRAPH
Ting Zhang, Muchun Li, Baogeng Xu, Ergeng Liu, Chao Zuo · 2007
A total coloring is called adjacent vertex distinguishing if every two adjacent vertices are incident to different sets of colored vertex and incident edge with vertex. The minimum number of colors required for a adjacent vertex distinguishing proper total coloring, a simple graph G is denoted byat(G). Let G(V,E) be a simple graph. If V (D(G)) = V (G) ( V (G 0 ), E(D(G)) = E(G) ( E(G 0 ) ( f viv 0 j vi 2 V (G),v 0 2 V (G 0 ) and vivj 2 E(G)g , then we call D(G) is the double graph of G graph,where G 0 is the copy of G. The paper studies the adjacent vetex distinguishing total chromatic number of Cn of D(G).