Graph coloring is an important tool in the study of optimization, computer science, network design, e.g., file transferring in a computer network, pattern matching, computation of Hessians matrix and so on. In this paper, we consider one important coloring, vertex coloring of a total graph, which is also called total coloring. We consider a planar graph G with maximum degree △（G） 〉 8, and proved that if G contains no adjacent i,j-cycles with two chords for some i,j E {5,6,7}, then G is total-（△ ＋ 1）-colorable.
Hui Juan WANGZhao Yang LUOBin LIUYan GUHong Wei GAO
