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《Quaestiones Mathematicae》2013,36(4):371-381
ABSTRACT The circulant graph Cp > a1,…, ak < with 0 > a1 >…> ak >(pt1)/2 has p vertices labeled 0,1,…,p-1 and x and y are adjacent if and only if x—y = ± ai (mod p) for some i. We prove the following regarding the chromatic index of a circulant: if d = gcd (a1,…, ak, p), then x' (Cp > al,…,ak) = Δ(C p > a1,…,ak) if and only if p/d is even. 相似文献
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《Quaestiones Mathematicae》2013,36(4):381-385
ABSTRACT A connected, nontrivial, simple graph of order v is said to be α,β destructible if α,β are integral factors of v and an α-set of edges, E', exists whose removal from G isolates exactly the vertices in a β-set V'. Graphs which are not α, β destructible for any α.β are called stable. In this paper we prove that all graphs on a non-prime number v of vertices are α,β destructible for some a which divides v. 相似文献
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《Quaestiones Mathematicae》2013,36(2):175-178
ABSTRACT A connected, nontrivial, simple graph of order v is said to be α,β destructible if α,β are factors of v and an α-set of edges, E', exists whose removal from G isolates exactly the vertices in α,β-set V'. Graphs which are not α,β destructible for any α,β are called stable, If G is a stable graph on a prime number p ≥ 7 of vertices, then we show that G has a maximum number of edges if and only if G is K2,p-2, We also characterize stable graphs on a minimum number of edges. 相似文献
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研究半导体方程解的整体性质,应用Stampacchia的最大模估计方法,证明了解的上下界整体估计. 相似文献
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Li Deming Liu YanpeiDept. of Math. Capital Normal Univ. Beijing . Email: lidm @ mail.cnu.edu.cn Dept. of Math. Northern Jiaotong Univ. Beijing . 《高校应用数学学报(英文版)》2000,(4)
§ 1 IntroductionThe maximum genusγM(G) of a graph G is the maximum among the genera,which Ghas a cellularembedding on a sphere with k handles.Since any embedding of G has atleastone face,by Euler polyhedral equation,itcan be obtained thatγM(G)≤β(G) / 2 ,whereβ(G) is the Betti number of G.A graph G is called up-embeddable ifγM(G) =β(G) / 2 .[1 ] has showed that thereare atleasttwo edge-disjointspanning trees in G if G is 4 -edge connected.Let T be a span-ning tree of G.An odd … 相似文献
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设α(G)表示简单图G=(V,E)的独立数.本文给出了α(G)的一个新的下界:α(G)≥∑v∈V(λd(v)+1)/(d(v)+λd(v)+1),其中λd(v)=max{0,βN(v)-d(v)},d(v)=|N(v)|,N(v)={w∈V|(v,w)∈E},βN(v)=minw∈N(v)d(w). 相似文献
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《Quaestiones Mathematicae》2013,36(1-2):291-313
Abstract A 0-dominating function 0DF of a graph G = (V,E) is a function f: V → [0,1] such that Σ xεN(v) f(x) ≥ 1 for each ν ε V with f(v) = 0. The aggregate of a 0DF f is defined by ag(f) = ΣvεV f(v) and the infimum and supremum of the set of aggregates over all minimal 0DFs of a graph are denoted by γ0 and Γ0 respectively. We prove some properties of minimal 0DFs and determine γ0 and Γ0 for some classes of graphs. 相似文献
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本文研究了空间曲面的等周亏格问题.利用R3中卵形区域的高斯曲率K及著名的等周小等式,得到R3中卵形区域的等周亏格的几个上界估计. 相似文献
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《Quaestiones Mathematicae》2013,36(1-2):275-289
Abstract Numerical solution of the wave equation in the form of close lower and upper bounds provides a secure a posteriori error estimate that can be used for efficient accuracy control. The method considered in this paper uses some monotone properties of the differential operator in the wave equation to construct bounds for the solution in the form of trigonometric polynomials of x. Aspects of the numerical implementation, the accuracy of the computed bounds and some numerical examples are discussed. 相似文献
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树的四类控制参数的束缚数 总被引:4,自引:0,他引:4
图的束缚数是图的控制数研究中的一个重要方面,它在某种程度上反映了图的控制数对边数的敏感度.本文通过对图的结构特征的分析.研究了树的四类控制参数的束缚数,即控制数,强控制数,弱控制数.分数控制数的束缚数.分别给出了其紧的上界. 相似文献