On the adjacent-vertex-strongly-distinguishing total coloring of graphs

查看全文 作　　者：ZHANG [1,2]ZhongFu;CHENG [1]Hui;YAO [1]Bing;LI [3]JingWen;CHEN [1]XiangEn;XU [4]BaoGen

机构地区：[1]College of Mathematics and Information Science,Northwest Normal University,Lanzhou,730070,China;[2]Institute of Applied Mathematic,Lanzhou Jiaotong University,Lanzhou 730070,China;[3]Department of Computer Science,Lanzhou Jiaotong University,Lanzhou 730070,China;[4]Department of Mathematics,East China Jiaotong University,Nanchang 330013,China

出　　处：《Science China Mathematics》索引2008年第51卷第3期,共10页

基　　金：the National Natural Science Foundation of China (Grant Nos. 10771091, 10661007) 摘　　要：For any vertex u∈V(G), let T_N(U)={u}∪{uv|uv∈E(G), v∈v(G)}∪{v∈v(G)|uv∈E(G)}and let f be a total k-coloring of G. The total-color neighbor of a vertex u of G is the color set C_f(u)={f(x)|x∈TN(U)}. For any two adjacent vertices x and y of V(G)such that C_f(x)≠C_f(y), we refer to f as a k-avsdt-coloring of G('avsdt'is the abbreviation of'adjacent-vertex-strongly- distinguishing total'). The avsdt-coloring number of G, denoted by X_ast(G), is the minimal number of colors required for a avsdt-coloring of G. In this paper, the avsdt-coloring numbers on some familiar graphs are studied, such as paths, cycles, complete graphs, complete bipartite graphs and so on. We proveΔ(G)+1≤X_ast(G)≤Δ(G)+2 for any tree or unique cycle graph G. 关键词：simple connected graph PROPER COLORING adjacent-vertex-strongly-distinguishing total COLORING

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On the adjacent-vertex-strongly-distinguishing total coloring of graphs

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