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【期刊论文】Small Regular Graphs Having the Same Path Layer Matrix
杨元生, Yang Yuansheng, * Lin Jianhua, and Wang Chunli
,-0001,():
-1年11月30日
The path layer matrix of graph G contains quantitative information about all paths in G. The entry (i,j) in this matrix is the number of simple paths in G having initial vertexi and length j. Some new upper bounds for r-regular graphs with the same path layer matrix are presented for r=4, 5, 6.
path layer matrix, degree sequence, regular graph
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【期刊论文】Harmonious Graphs C2k SC2j+1*
杨元生, Yang Yuanshengm, , Lin Xiaohui, Lu Weiming, Zeng Qingshuang
,-0001,():
-1年11月30日
In this article, we show that the disjoint union C2k UC2j+1 of cycles C2k and C2j+1 (k
Harmonious Graphs,, harmonious labelling,, edge label,, vertex label
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【期刊论文】Extremal Graphs Without Three-Cycles, Four-Cycles or Five-Cycles*
杨元生, Yang Yuansheng, Lin Xiaohui, Dong Guocheng, Zhao Yongxiang
,-0001,():
-1年11月30日
Given a set of graphs Ψ={G1, G2, …, Gk}, let ex(n; Ψ) denote the greatest size of a graph with order n that contains no subgraph isomorphic to some Gi, 1≤i≤k. One of the main classes of problems in extremal graph theory, known as Tuŕan-type problems, is for given n, Ψ to determine explicitly the function ex (n, Ψ), or to find its asymptotic behavior. Yang Yuansheng investigated the values of ex(n, Ψ) for Ψ={C4} (UTILITAS MATHEMATICA, 41 (1992), 204-210), Garnick investigated them for Ψ={C3, C4} (Journal of Graph Theory, vol.17, no.5 (1993), 633-645) and Alabdullatif investigated them for Ψ={Cn-k+1, …, Cn and Ψ={Pn-k+1,…, Pn}, (1≤k≤n-2) (Bull. Inst. Combin. Appl., 25 (1999)41-52). This paper investigates the values of ex (n, Ψ) forΨ={C3, C4, C5}, n≤42.
extremal graph,, forbidden subgraph,, cage,, girth
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【期刊论文】4-Regular Graphs Without Cut-Vertices Having the Same Path Layer Matrix
杨元生, Yang Yuansheng, * Lin Xiaohui, Chen Zhiqiang, and Lu Weiming
,-0001,():
-1年11月30日
The path layer matrix of a graph G contains quantitative information about all possible paths in G. The entry (i; j ) of this matrix is the number of paths in G having initial vertex i and length j. It is known that there are 4-regular graphs on 44 vertices having the same path layer matrix[Y. Yuansheng, L. Jianhua, and W. Chunli, J Graph Theory 39(2002) 219-221] graphs with cut-vertices on 14 vertices having the same path layer matrix [A. A. Dobrynin, Vyčisl. sistemy, Novosibirsk 119(1987) 13-33] and graphs without cut-vertices on 31 vertices having the same path layer matrix [A. A. Dobrynin, J Graph Theory 38(2001) 177-182]. In this article, a pair of 4-regular graphs without cut-vertices on 18 vertices having the same path layer matrix are constructed, improving the upper bound for the least order of 4-regular graphs having the same path layer matrix from 44 to 18 and the upper bound for the least order of graphs without cut-vertices having the same path layer matrix from 31 to 18.
undirected graph, path, path layer matrix, graph isomorphism
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杨元生, , 王丹, 陆维明
软件学报,2002,13(12):1~8,-0001,():
-1年11月30日
利用计算机对图的交叉数进行研究,给出利用分支界限法计算图的交叉数的算法CCN(calculate crossing Number),并利用该算法计算出n≤12的所有四正则图的交叉数,以及n≤16的随机四正则的交叉数。同时计算出n≤12的所有四正则图的平均交叉数Aac(n),和n≤16的随机四正则图的平均交叉数Arc(n),根据计算结果提出四正则图的平均交叉数为O(n2)的猜想。
交叉数, 正则图, 同构, 平面图, 分支界限法
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