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C_3n²,C_4n²邻点可区别的全染色

Adjacent Vertex-Distinguishing Total Colorings of C_3n² and C_4n²

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【Author】 Ma Shengquan 1,Zhang Zhongfu 2,Yao Bing 3,Li Jingwe n 4(1. Dept.of Math.Northwest Minorith University,Lanzhou730030,China;2. Institute of Applied Mathematics,Lanzhou Jiaotong University,Lanzhou730070, China;3. Dept.of Mathematics,Northwest Normal University,Lanzhou730070,China;4. College of Information and Electrical Engineering,Lanzhou Jiaotong University ,Lanzhou730070,China.)

【机构】西北民族大学数学系；兰州交通大学应用数学研究所；西北师范大学数学系；兰州交通大学信息与电气工程学院甘肃兰州730030；甘肃兰州730070；甘肃兰州730070；

【摘要】设G(V ,E)是阶数不小于 2的简单连通图 ,n是自然数 ,V∪E到 { 1,2 ,… ,k}的映射f满足 uv∈E(G) ,f(u)≠f(v) ,f(u)≠f(uv) ≠f(v) ; uv,uw∈E(G) ,(v≠w) ,f(uv)≠f(uw) ; uv∈E(G) ,G(u) ≠C(v) .其中C(u) =f(u) ∪ {f(uv)｜uv∈E(G) } .f称为G(V ,E)的一个邻点是可区分的全染色法 ,简记为k AVDTC .其中最小的k称为G的邻点可区别的全色数 .G2 是G再加上G中点间距离为 2时连边后的图 .本文得到了 3n、4n阶圈C23n,C24n 的邻点可区别的全色数 .更多还原

【Abstract】 A total-coloring is called adjacent vertex-disti nguishing 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 an adjacent vertex-distinguishing proper total-coloring a simple graph G is denot ed byχ at (G).We prove thatχ at (C 2 3n )=6 (n≥2).and kat (C4n 2)=6(n≥8)WhereC 2 3n is cycle C 3n and its edge of two vertices distance are 2 .更多还原