共查询到20条相似文献,搜索用时 943 毫秒
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本文证明了若G是连通、局部连通的无爪图,则G是泛连通图的充要条件为G是3-连通图.这意味着H.J.Broersma和H.J.Veldman猜想成立. 相似文献
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4连通图的可去边与4连通图的构造 总被引:2,自引:0,他引:2
本文引进了4连通图的可去边的概念,,并证明了4连通图G中不存在可去边的充要条件是G=C5或C6,同时给出了n阶4连通图的一个新的构造方法. 相似文献
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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 the deletion of each minimum vertex cut creates exactly two components, one of which is an isolated vertex. In this note,
we proved that a vertex transitive bipartite graph is not super-connected if and only if it is isomorphic to the lexicographic
product of a cycle Cn(n ≥ 6) by a null graph Nm. We also characterized non-hyper-connected vertex transitive bipartite graphs. 相似文献
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A digraph is said to be super-connected if every minimum vertex cut is the out-neighbor set or in-neighbor set of a vertex. A digraph is said to be reducible, if there are two vertices with the same out-neighbor set or the same in-neighbor set. In this paper, we prove that a strongly connected arc-transitive oriented graph is either reducible or super-connected. Furthermore, if this digraph is also an Abelian Cayley digraph, then it is super-connected. 相似文献
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Bi-Cayley图的一些代数性质 总被引:1,自引:0,他引:1
设G是一个有限群,S是G的一个子集,Bi-Cayley图BC(G,S)是一个二部图:其顶点集为G×{0,1},而边集为{{(g,0),(sg,1)}:g∈G,s∈S}.本文研究了有限阿贝尔群G上的Cayley图D(G,S)和Bi-Calyley图BC(G,S)之间特征值的关系,并由此得到循环群上的Bi-Cayley图的特征值.继而得到生成树数的一些渐进性定理. 相似文献
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Zhao Zhang 《Discrete Mathematics》2006,306(7):705-710
A graph G is said to be hyper-connected if the removal of every minimum cut creates exactly two connected components, one of which is an isolated vertex. In this paper, we first generalize the concept of hyper-connected graphs to that of semi-hyper-connected graphs: a graph G is called semi-hyper-connected if the removal of every minimum cut of G creates exactly two components. Then we characterize semi-hyper-connected edge transitive graphs. 相似文献
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A graph G is said to be super-connected if any minimum cut of G isolates a vertex. In a previous work due to the second author of this note, super-connected graphs which are both vertex transitive and edge transitive are characterized. In this note, we generalize the characterization to edge transitive graphs which are not necessarily vertex transitive, showing that the only irreducible edge transitive graphs which are not super-connected are the cycles Cn(n?6) and the line graph of the 3-cube, where irreducible means the graph has no vertices with the same neighbor set. Furthermore, we give some sufficient conditions for reducible edge transitive graphs to be super-connected. 相似文献
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图G称为上连通的,若对每个最小割集C,G-C有孤立点,G称为超连通的,若对每个最小割集C,G-C恰有两个连通分支,且其中之一为弧立点,本文刻划了上连通和超连通三次点传递图。 相似文献
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图G称为上连通的,若对每个最小割集C,G-C有孤立点.G称为超连通的,若对每个最小割集G,G-C恰有两个连通分支,且其中之一为孤立点.本文刻划了上连通和超连通三次点传递图. 相似文献
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图是超限制性边连通的充分条件 总被引:1,自引:0,他引:1
设G=(V,E)是连通图.边集S E是一个限制性边割,如果G-S是不连通的且G—S的每个分支至少有两个点.G的限制性连通度λ'(G)是G的一个最小限制性边割的基数.G是λ'-连通的,如果G存在限制性边割.G是λ'-最优的,如果λ'(G)=ζ(G),其中ζ(G)是min{d(x)+d(y)-2:xy是G的一条边}.进一步,如果每个最小的限制性边割都孤立一条边,则称G是超限制性边连通的或是超-λ'.G的逆度R(G)=∑_(v∈V) 1/d(v),其中d(v)是点v的度数.我们证明了G是λ'-连通的且不含三角形,如果R(G)≤2+1/ζ-ζ/((2δ-2)(2δ-3))+(n-2δ-ζ+2)/((n-2δ+1)(n-2δ+2)),则G是超-λ'. 相似文献
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A strongly connected digraph D is said to be super-connected if every minimum vertex-cut is the out-neighbor or in-neighbor set of a vertex. A strongly connected digraph D is said to be double-super-connected if every minimum vertex-cut is both the out-neighbor set of a vertex and the in-neighbor set of a vertex. In this paper, we characterize the double-super-connected line digraphs, Cartesian product and lexicographic product of two digraphs. Furthermore, we study double-super-connected Abelian Cayley digraphs and illustrate that there exist double-super-connected digraphs for any given order and minimum degree. 相似文献
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Let N denote the set of positive integers.The sum graph G (S) of a finite subset S (C) N is the graph (S,E) with uv ∈ E if and only if u v ∈ S.A graph G is said to be a sum graph if it is isomorphic to the sum graph of some S С N.By using the set Z of all integers instead of N,we obtain the definition of the integral sum graph.A graph G=(V,E) is a mod sum graph if there exists a positive integer z and a labelling,λ,of the vertices of G with distinct elements from {0,1,2,...,z-1} so that uv ∈ E if and only if the sum,modulo z,of the labels assigned to u and v is the label of a vertex of G.In this paper,we prove that flower tree is integral sum graph.We prove that Dutch m-wind-mill (Dm) is integral sum graph and mod sum graph,and give the sum number of Dm. 相似文献