共查询到18条相似文献,搜索用时 62 毫秒
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本文给出了一种构造给定直径d和围长g的测地块的方法,它是文(1)中构造法的推广,解决了文(1)中待研究的几个问题,同时对文(1)中的一错误进行了修正。 相似文献
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本文给出了一种新的测地块的构造方法,这种方法不同于已有的所有方法,它是由BD设计和某些已知的测地块来构造的。同时肯定地回答了Plesnik提出是否存在不同于WPd和Kn^(i)的测地块的问题。 相似文献
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测地块的测地临界性 总被引:1,自引:0,他引:1
毛经中 《数学物理学报(A辑)》1992,(4)
本文证明了所有测地块都是上测地临界的,而且所有不与任何奇圈同构的测地块都是下测地临界的。因而Pathasarathy-Srinivasan猜想为真。 相似文献
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测地块的测量地临界性 总被引:2,自引:0,他引:2
毛经中 《数学物理学报(A辑)》1992,12(4):407-411
本文证明了所有测地块都是上测地临界的,而且所有不与任何奇圈构的测地块都是下地临界的。因而Pathasarathy-Srinivasan猜想为真。 相似文献
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主要讨论了群环Z_nG的基于理想△(G)的零因子图Γ_(△(G))(Z_nG)的性质,分别给出了Γ_(△(G))(Z_nG)的围长,平面性和直径的详细刻画.同时,给出了交换环R基于其理想I的零因子图Γ_I(R)与商环R/I的零因子图Γ(R/I)的直径的关系的一个刻画. 相似文献
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《数学的实践与认识》2013,(18)
研究了与频道分配有关的一种染色-(p,1)-全标号.通过在一个顶点粘结不同的简单图构造了几类有趣图,根据所构造图的特征,利用穷染法,给出了一种标号方法,得到了平凡和非平凡叶子图Gm,4、风车图K3t和图Dm,n的(2,1)-全标号数.(p,1)-全标号是对图的全染色的一种推广. 相似文献
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具体刻画了柱面、锥面、旋转曲面上测地线的几何特征,所得结果一方面匡正了某些文献关于锥面上测地线的错误断言,一方面推广了现有文献关于旋转曲面上测地线几何性质的描述. 相似文献
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A vertex-cut X is said to be a restricted cut of a graph G if it is a vertex-cut such that no vertex u in G has all its neighbors in X. Clearly, each connected component of G−X must have at least two vertices. The restricted connectivity κ′(G) of a connected graph G is defined as the minimum cardinality of a restricted cut. Additionally, if the deletion of a minimum restricted cut isolates one edge, then the graph is said to be super-restricted connected. In this paper, several sufficient conditions yielding super-restricted-connected graphs are given in terms of the girth and the diameter. The corresponding problem for super-edge-restricted-connected graph is also studied. 相似文献
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Ostrand posed the following two questions in 1973. (1) What is the maximum girth of a graph with radius
and diameter ? (2) What is the minimum circumference of a graph with radius
and diameter ? Question 2 has been answered by Hrn?iar who proves that if the minimum circumference is In this note we first answer Question 1 by proving that the maximum girth is This improves on the obvious upper bound
and implies that every Moore graph is self-centered. We then prove a property of the blocks of a graph which implies Hrn?iar’s result. 相似文献
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变换图的直径及Brualdi猜想 总被引:1,自引:0,他引:1
设R=(r1,r2…rm)及 S=(S1,S2,…,Sn)为两个正整数向量,满足Σmi=1ri=Σnj=1sj= K.记G(R,S)为(0,1)-矩阵类 U(R,S)的变换图.Brualdi在文山中给出了 G(R,S)的直径厂(G(R,S))的一个上界:mn/2-1,并猜想D(G(R,S))≤mn/4.本文通过对有向图围长的研究得到了D(G(R,S))的一个新的上界:1/2mn-1/6t(t-1)(4t+1),其中T= . 相似文献
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In this paper, first we prove that any graph G is 2-connected if diam(G)≤g−1 for even girth g, and for odd girth g and maximum degree Δ≤2δ−1 where δ is the minimum degree. Moreover, we prove that any graph G of diameter diam(G)≤g−2 satisfies that (i) G is 5-connected for even girth g and Δ≤2δ−5, and (ii) G is super-κ for odd girth g and Δ≤3δ/2−1. 相似文献
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C. Balbuena 《Discrete Mathematics》2007,307(6):659-667
The restricted connectivity κ′(G) of a connected graph G is defined as the minimum cardinality of a vertex-cut over all vertex-cuts X such that no vertex u has all its neighbors in X; the superconnectivity κ1(G) is defined similarly, this time considering only vertices u in G-X, hence κ1(G)?κ′(G). The minimum edge-degree of G is ξ(G)=min{d(u)+d(v)-2:uv∈E(G)}, d(u) standing for the degree of a vertex u. In this paper, several sufficient conditions yielding κ1(G)?ξ(G) are given, improving a previous related result by Fiol et al. [Short paths and connectivity in graphs and digraphs, Ars Combin. 29B (1990) 17-31] and guaranteeing κ1(G)=κ′(G)=ξ(G) under some additional constraints. 相似文献
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Stephen E. Wright 《代数通讯》2013,41(6):1987-1991
Short, elementary proofs of the optimal bounds for various path and cycle lengths are given for the zero-divisor graphs and digraphs of semigroups. 相似文献
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A graph is superconnected, for short super-κ, if all minimum vertex-cuts consist of the vertices adjacent with one vertex. In this paper we prove for any r-regular graph of diameter D and odd girth g that if D≤g−2, then the graph is super-κ when g≥5 and a complete graph otherwise. 相似文献