共查询到17条相似文献,搜索用时 78 毫秒
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几类图的匹配等价图类 总被引:1,自引:0,他引:1
魏岭 《数学的实践与认识》2011,41(17)
两个图G和H的匹配多项式相等,则称它们匹配等价.用[G]表示图G的所有不同构的匹配等价图的集合.刻画了匹配次大根小于1的图及这些图的补图的匹配等价图类. 相似文献
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匹配最大根小于等于2的图的匹配等价 总被引:2,自引:0,他引:2
给出了十六个匹配等价桥,证明了两个匹配最大根小于等于2的图匹配等价当且仅当它们之间可以由这十六个匹配等价桥进行等价转换,完整地刻画了这些图的补图的匹配等价图类,找到了这些图和它们的补图中的所有匹配唯一图. 相似文献
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几类图的匹配多项式之间的关系与一类图的匹配等价图 总被引:1,自引:0,他引:1
张海良 《纯粹数学与应用数学》2007,23(2):178-182
研究了几类图的匹配多项式以及它们之间的一些整除关系,给出了路的匹配多项式相互整除的一个充分必要条件,并且刻画了图T2,2,n的所有匹配等价图. 相似文献
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利用图的匹配多项式及其最大实数根的性质完整刻画了T(2,2,n)∪(∪i∈A Ci)(n≥3,A是大于等于3的整数组成的可重集)的匹配等价图类. 相似文献
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利用图的匹配多项式及其最大实数根的性质完整刻画了T(2,2,n)U(U C<,t>)(n≥3,A是大于等于3的整数组成的可重集)的匹配等价图类. 相似文献
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Let G be a graph with n(G) vertices and m(G) be its matching number.The nullity of G,denoted by η(G),is the multiplicity of the eigenvalue zero of adjacency matrix of G.It is well known that if G is a tree,then η(G) = n(G)-2m(G).Guo et al.[Jiming GUO,Weigen YAN,Yeongnan YEH.On the nullity and the matching number of unicyclic graphs.Linear Alg.Appl.,2009,431:1293 1301]proved that if G is a unicyclic graph,then η(G)equals n(G)-2m(G)-1,n(G)-2m(G),or n(G)-2m(G) +2.In this paper,we prove that if G is a bicyclic graph,then η(G) equals n(G)-2m(G),n(G)-2m(G)±1,n(G)-2m(G)±2or n(G)-2m(G) + 4.We also give a characterization of these six types of bicyclic graphs corresponding to each nullity. 相似文献
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Alberto Alexandre Assis Miranda Cláudio Leonardo Lucchesi 《Discrete Applied Mathematics》2010,158(12):1275-1278
A matching covered graph is a non-trivial connected graph in which every edge is in some perfect matching. A non-bipartite matching covered graph G is near-bipartite if there are two edges e1 and e2 such that G−e1−e2 is bipartite and matching covered. In 2000, Fischer and Little characterized Pfaffian near-bipartite graphs in terms of forbidden subgraphs [I. Fischer, C.H.C. Little, A characterization of Pfaffian near bipartite graphs, J. Combin. Theory Ser. B 82 (2001) 175-222.]. However, their characterization does not imply a polynomial time algorithm to recognize near-bipartite Pfaffian graphs. In this article, we give such an algorithm.We define a more general class of matching covered graphs, which we call weakly near-bipartite graphs. This class includes the near-bipartite graphs. We give a polynomial algorithm for recognizing weakly near-bipartite Pfaffian graphs. We also show that Fischer and Little’s characterization of near-bipartite Pfaffian graphs extends to this wider class. 相似文献
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A graph G is induced matching extendable if every induced matching of G is included in a perfect matching of G. A graph G is generalized induced matching extendable if every induced matching of G is included in a maximum matching of G. A graph G is claw-free, if G dose not contain any induced subgraph isomorphic to K1,3. The k-th power of G, denoted by Gu, is the graph with vertex set V(G) in which two vertices are adjacent if and only if the distance between them is at most k in G. In this paper we show that, if the maximum matchings of G and G3 have the same cardinality, then G3 is generalized induced matching extendable. We also show that this result is best possible. As a result, we show that if G is a connected claw-flee graph, then G3 is generalized induced matching extendable. 相似文献
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申世昌 《纯粹数学与应用数学》2008,24(1):107-110
讨论简单无向图G的匹配唯一性,研究T形树T(m,n,s)匹配唯一的充分条件.利用匹配多项式根的信息,根据其定义以及图的度序列和匹配多项式的性质推导.若T形树T(m,n,s)是几乎等长的,则其是匹配唯一的.找到了T形树T(m,n,s)匹配唯一的一个充分条件,并得到了图的匹配多项式根的一些性质. 相似文献
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V.V. Mkrtchyan 《Discrete Mathematics》2006,306(4):452-455
A graph is called matching covered if for its every edge there is a maximum matching containing it. It is shown that minimal matching covered graphs without isolated vertices contain a perfect matching. 相似文献
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利用图的匹配多项式及其最大实数根的性质证明了树T(1,1,n,2,1)及补图匹配唯一的充要条件是n≠1,2,5,8. 相似文献