共查询到20条相似文献,搜索用时 125 毫秒
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图Γ称为点传递自补图,如果Γ的图自同构群AutΓ在顶点集合VΓ作用是传递的,且Γ的补图(Γ)与图Γ是同构的.本文主要研究了通过Cayley同构来构造点自补Cayley图,并证明了内循环群上的这类图必然是循环自补图. 相似文献
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4K+1阶强正则自补图的存在唯一性 总被引:2,自引:1,他引:1
4k+1阶强正则自补图的存在唯一性刘象武(哈尔滨师范大学数学系哈尔滨150080)关键词:循环图;强正则自补图;原根AMS(1991)主题分类:05E30.本文所述的图均指有限无向简单图.本文分别用字母户,庄,人和产表示强正则图的顶点数、正则度、两相... 相似文献
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本文所用的概念与符号与文献[2]相同,不相同的定义如下。 设G是一个自补图(下称s.c.图),p是G到它的补图G的同构映射,则称p是G的一个自补置换(下简称为s.c.置换)。我们用符号P(G)表示s.c.图G的全体s.c.置换的集合。设p∈P(G),若p是m个轮换的乘积,则记p=p_1p_2…pm,并记pi的长为|pi|。 相似文献
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许进 《数学物理学报(A辑)》1996,(Z1)
该文证明了具有p个顶点的自补图中三角形的数目至多是,当p≡0(Mod4)时为p(p-4)(2p-1)/48,当p≡1(mod4)时为(p-1)(2p2-7p-3)/48,并且此二数是最好可能的. 相似文献
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J.Akiyama和F.Harary提出:是否存在非自补图G,使得G与其补图有相同的色多项式,本文给出一个肯定的回答,并证明了:这样的平面图G仅存在有限多个。 相似文献
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图与其补图谱半径之间的关系 总被引:6,自引:0,他引:6
徐寅峰 《纯粹数学与应用数学》1993,9(2):89-90
本文我们将图与其补图结合起来,给出了图与其补图的谱半径所必须满足的两个不等式。 相似文献
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图与其补图谱半径之间关系的注记 总被引:9,自引:0,他引:9
周波 《纯粹数学与应用数学》1997,13(1):15-18
给出在一般情形和某些限制条件下图及其补图的谱半径的和与积的上界,改进了文[1]的结果。 相似文献
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Primo? Poto?nik 《Discrete Mathematics》2006,306(1):107-123
A graph is called almost self-complementary if it is isomorphic to one of its almost complements Xc-I, where Xc denotes the complement of X and I a perfect matching (1-factor) in Xc. Almost self-complementary circulant graphs were first studied by Dobson and Šajna [Almost self-complementary circulant graphs, Discrete Math. 278 (2004) 23-44]. In this paper we investigate some of the properties and constructions of general almost self-complementary graphs. In particular, we give necessary and sufficient conditions on the order of an almost self-complementary regular graph, and construct infinite families of almost self-complementary regular graphs, almost self-complementary vertex-transitive graphs, and non-cyclically almost self-complementary circulant graphs. 相似文献
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Kotzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongly-regular self- complementary graph whose order is 4k 1, where 4k 1=x2 y2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k 1 orders. 相似文献
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We prove that the automorphism group of a self-complementary metacirculant is either soluble or has \(\mathrm{A}_5\) as the only insoluble composition factor, extending a result of Li and Praeger which says the automorphism group of a self-complementary circulant is soluble. The proof involves a construction of self-complementary metacirculants which are Cayley graphs and have insoluble automorphism groups. To the best of our knowledge, these are the first examples of self-complementary graphs with this property. 相似文献
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We briefly describe how we compiled a catalog of all the 720 self-complementary graphs on 12 nodes. In our first attempt at this compilation one graph was inadvertently omitted. The missing graph was subsequently found by making use of a theoretical formula due to Parthasarathy and Sridharan for counting self-complementary graphs with given partitions. 相似文献
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A construction is given of an infinite family of finite self-complementary,vertex-transitive graphs which are not Cayley graphs. To theauthors' knowledge, these are the first known examples of suchgraphs. The nature of the construction was suggested by a generalstudy of the structure of self-complementary, vertex-transitivegraphs. It involves the product action of a wreath product ofpermutation groups. 2000 Mathematics Subject Classification05C25. 相似文献
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Richard A Gibbs 《Journal of Combinatorial Theory, Series B》1974,16(2):106-123
In this paper a new algorithm is given for the construction of self-complementary graphs, and results concerning structural properties and adjacency matrices of these graphs are presented. 相似文献
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We characterize the class of self-complementary vertex-transitive digraphs on a prime number p of vertices. Using this, we enumerate (i) self-complementary strongly vertex-transitive digraphs on p vertices, (ii) self-complementary vertex-transitive digraphs on p vertices, (iii) self-complementary vertex-transitive graphs on p vertices. Finally it is shown that every self-complementary vertex-transitive digraph on p vertices is either a tournament or a graph. 相似文献
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Cai Heng Li 《代数通讯》2013,41(12):3903-3908
In this paper we study the problem of determining positive integers n for which there exist self-complementary vertex-transitive graphs of order n. The main aim of this paper is to prove that, for distinct primes p, q, there exist self-complementary vertex-transitive graphs of order pq if and only if p, q Scz.tbnd;1 (mod 4). This provides negative answers to a long-standing open question proposed by Zelinka (1979) and a recent open question proposed by Froncek, Rosa Siran (1996). 相似文献
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Hong Zhang 《Journal of Graph Theory》1992,16(1):1-5
The class of self-complementary symmetric graphs is characterized using the classification of finite simple group. 相似文献
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C. R. J. Clapham 《Journal of Graph Theory》1979,3(3):287-289
A method is described of constructing a class of self-complementary graphs, that includes a self-complementary graph, containing no K5, with 41 vertices and a self-complementary graph, containing no K7, with 113 vertices. The latter construction gives the improved Ramsey number lower bound r(7, 7) ≥ 114. 相似文献