共查询到17条相似文献,搜索用时 46 毫秒
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首先对开关图的自同构群进行了研究,随即讨论了它的点传递性,并得到Calyley图的开关图依然是Cayley图. 相似文献
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边覆盖临界图的一些性质 总被引:2,自引:0,他引:2
设G是一个简单图,其顶点集为V(G)而边集为E(G),S∈E(G)称为 G的一个覆盖,如果由S导出的子图为G的一个生成子图. G的边覆盖色数χ'c(G)是E(G,)所能划分成的最大边覆盖数.已知δ-1 ≤χ'c(G)≤δ,由此将χ'c(G)=δ的图称为CI类图,否则称为CII类图.若G是连通CII类图,且G不是完全图,对任意的u,u∈V(G),e=uv( )E(G),都有χ'c(G+e)>χ'c(G)成立,则称G为边覆盖临界的.本文研究了边覆盖临界图的一些性质.即若G为边覆盖临界图,则对任意的u,v∈V(G),若e=uv( )E(G),总存在w∈{u,v},有d(w)≤2δ-2,且w至少与max{d(w)-δ+1,3d(w)-4δ+4}个最小度顶点相邻. 相似文献
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若一个图能够由某一个或某几个运算作用于不相交的图上而得到,则称该图为复合图.记t(G)为图G的生成树个数,H(G)为图G的Kirchhoff矩阵,用“o”表示图的某种运算,如“+”,“×”,“合成”等,本文研究了H(GoG′)与H(G),H(G′)的特征值关系,给出了t(GoG′)的一般性公式,提供了几种复合图生成树个数的一般性公式,提供了几种复合图生成树个数的一般求法,大大推广了[2,3]的结果,同时简化了许多图类生成树个数表达式的求法. 相似文献
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正规矩阵的若干性质 总被引:3,自引:0,他引:3
宋永忠 《纯粹数学与应用数学》1992,8(1):113-116
众所周知,Hermite矩阵有许多较好的性质,其中多数性质对一般矩阵是不成立的。然而,对一类常见的特殊矩阵—正规矩阵,却有着类似的性质。本文就来对此进行一些研究。 相似文献
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Let G be a finite group and let S(possibly, contains the identity element) be a subset of G. The Bi-Cayley graph BC(G, S) is a bipartite graph with vertex set G×{0, 1} and edge set {(g, 0) (sg, 1) : g∈G, s ∈ S}. A graph is said to be super-connected if every minimum vertex cut isolates a vertex. A graph is said to be hyper-connected if every minimum vertex cut creates two components, one of which is an isolated vertex. In this paper, super-connected and/or hyper-connected cubic Bi-Cayley graphs are characterized. 相似文献
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证明了在复对称算子的前提下,对数-亚正规算子与正规算子是等价的,并且给出了复对称算子的一些等价性质;最后通过给出例子来说明我们的结论. 相似文献
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本文中我们证明几个关于克希霍夫矩阵的新定理.在这些定理下,代数图论中Temperly,Kelmans,以及Fiedler提出的一些早期定理成为直接的推论. 相似文献
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Yanfeng Luo 《Discrete Mathematics》2009,309(20):5943-1987
Let G be a finite group and A a nonempty subset (possibly containing the identity element) of G. The Bi-Cayley graph X=BC(G,A) of G with respect to A is defined as the bipartite graph with vertex set G×{0,1} and edge set {{(g,0),(sg,1)}∣g∈G,s∈A}. A graph Γ admitting a perfect matching is called n-extendable if ∣V(Γ)∣≥2n+2 and every matching of size n in Γ can be extended to a perfect matching of Γ. In this paper, the extendability of Bi-Cayley graphs of finite abelian groups is explored. In particular, 2-extendable and 3-extendable Bi-Cayley graphs of finite abelian groups are characterized. 相似文献
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We provide some exact formulas for the projective dimension and regularity of edge ideals associated to some vertex-weighted oriented cyclic graphs with a common vertex or edge.These formulas are functions in the weight of the vertices,and the numbers of edges and cycles.Some examples show that these formulas are related to direction selection and the assumption that w(x)≥2 for any vertex x cannot be dropped. 相似文献
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Let and denote the second largest eigenvalue and the maximum number of edge‐disjoint spanning trees of a graph G, respectively. Motivated by a question of Seymour on the relationship between eigenvalues of a graph G and bounds of , Cioab? and Wong conjectured that for any integers and a d‐regular graph G, if , then . They proved the conjecture for , and presented evidence for the cases when . Thus the conjecture remains open for . We propose a more general conjecture that for a graph G with minimum degree , if , then . In this article, we prove that for a graph G with minimum degree δ, each of the following holds.
- (i) For , if and , then .
- (ii) For , if and , then .
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若干图的广义Mycielski图的边色数 总被引:2,自引:1,他引:1
设图G(V,E)为简单图,V(Mn(G))={v01,v02,…,v0p;v11,v12,…,v1p;…,vn1,vn2,…,vnp}EMn(G))=E(G)∪vijv(i+1)kv0 jv0k∈E(G),1 j,k p,i=0,1,…,n-1称Mn(G)为G的n串广义M ycielsk i图,其中n为自然数,V(G)={v01,v02,…,v0p}.本文得到了路、圈、扇、轮、星图的广义M ycielsk i图的边色数. 相似文献