共查询到19条相似文献,搜索用时 453 毫秒
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一个图G的乘积离心率电阻距离ξ*R(G)是在图上的所有无序顶点对的顶点对应的离心率和顶点对之间的电阻距离的乘积的和.本文运用了图变换的方法,分别刻画了所有的n个顶点的单圈图中,具有最大、第二大、最小和第二小乘积离心率电阻距离的极值图.进一步,分别刻画了所有的n个顶点且给定最大度的单圈图中,具有最大、第二大和第三大乘积离心率电阻距离的极值图. 相似文献
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任给一个连通图,高芳等人首先引进了G的一个不变量?M(G)=Mo(G)-irr(G),并提出一个问题:怎样确定所有含n个顶点的连通图G的?M(G)的极值,其中Mo(G)和irr(G)分别表示G的Mostar指标和不规则度.本文针对这个问题,刻画所有直径为3的单圈图和双圈图G的?M(G)的上界,并给出它们的极图. 相似文献
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对连通图$G$的顶点$u$和$v$, $u$与$v$在$G$中的电阻距离$r_G(u,v)$等于相邻顶点之间的电阻为单位电阻的$G$对应的电网中$u$与$v$之间的等效电阻. 图$G$的电阻-距离特征值是$G$的电阻-距离矩阵$R(G)=(r_G(u,v))_{u,v\in V(G)}$的特征值. 我们分别确定了不同于完全图与完全图删去一条边后得到的图及给定割边数目的使得最大电阻-距离特征值取得最小值的唯一的连通图, 还讨论了最小电阻-距离特征值的性质. 相似文献
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2-控制数和连通2-控制数相等的图(英文) 总被引:1,自引:0,他引:1
任意一个图G =(V ,E) ,S是V(G)的子集 ,如果对每一个顶点u∈V-S都存在顶点v∈S ,使得d(u ,v) ≤ 2 ,则称S为G的一个 2 控制 .称最小的 2 控制集的顶点个数为G的 2 控制数 ,记为γ2 (G) .如果G的一个 2 控制集S的生成子集〈S〉是一个连通图 ,则称S为G的一个连通 2 控制集 .称最小的连通 2 控制集的顶点个数为G的连通 2 控制数 ,记为γc2 (G) .本文论述了树和单圈图中 2 控制数和连通 2 控制数相等的充分必要条件 . 相似文献
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Laplacian spread的概念在刻画图的整体性质方面非常重要.近年来,Fan等分别刻画了树中具有极大和极小Laplacian spread的图.另外Bao等确定了在所有单圈图中具有极大Laplacian spread的图.边数减去顶点数目为1的连通图称为双圈图.令B_n是所有有n个顶点构成的双圈图集合.对n≥11,本文确定了B_n中所有具有极大Laplacian spread的那些图. 相似文献
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n阶图G称为是一个单圈图,如果G是连通的,并且G的边数也是n.用U(n)表示所有n阶单圈图所成的集合.给出了当阶数n≥25时,代数连通度为前九大的n阶单圈图及它们的代数连通度. 相似文献
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如果在—个κ连通图G中删掉任意一个顶点后得到的图都不再是κ连通,则称G为临界κ连通.Chartrand,Kaugars和Lick证明了每一个临界κ连通图(κ≥2)都含有一个度数小于(3κ-1)/2的顶点.Hamidoune进一步证明了每一个临界k连通图都至少含有两个这样的顶点,并且这一下界是最优的.在本文中,我们证明如果一个临界κ连通图恰好含有两个度数小于(3κ-1)/2的顶点,则这两个顶点的度数一定是κ. 相似文献
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设U (n)是具有n个顶点的所有单圈图的集合,G(3; n- 3)是由一个三角形C3粘上一条悬挂路P_(n-3)得到的单圈图.本文将证明当n 5时具有最大度距离的单圈图是G(3; n - 3). 相似文献
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图G的广义Randic指标定义为Rα=Rα(G)=∑uv∈E(G)(d(u)d(v))^α,其中d(u)是G的顶点u的度,α是任意实数.本文确定了单圈共轭图的广义Randic指标R-1的严格下界,并刻划了达到最小R-1的极图,这类极图还是化学图. 相似文献
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令u(n)表示具有n个顶点的单圈图.在一个圈C3的一个顶点上悬挂n-3个悬挂边的n个顶点的单圈图记为U~*(n-3,0,0).本文证明了在u(n)中具有最小hyper-Wiener指数的单圈图是U~*(n-3,0,0). 相似文献
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In this paper, we characterize all extremal connected bicyclic graphs with the largest signless Laplacian spectral radius in the set of all connected bicyclic graphs with prescribed degree sequences. Moreover, the signless Laplacian majorization theorem is proved to be true for connected bicyclic graphs. As corollaries, all extremal connected bicyclic graphs having the largest signless Laplacian spectral radius are obtained in the set of all connected bicyclic graphs of order n (resp. all connected bicyclic graphs with a specified number of pendant vertices, and all connected bicyclic graphs with given maximum degree). 相似文献
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The hyper-Wiener index is a kind of extension of the Wiener index, used for predicting physicochemical properties of organic compounds. The hyper-Wiener index W W(G) is defined as WW(G) =1/2∑_(u,v)∈V(G)(d_G(u, v) + d_G~2(u,v)) with the summation going over all pairs of vertices in G, d_G(u,v) denotes the distance of the two vertices u and v in the graph G. In this paper,we study the minimum hyper-Wiener indices among all the unicyclic graph with n vertices and diameter d, and characterize the corresponding extremal graphs. 相似文献
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《Quaestiones Mathematicae》2013,36(4):533-549
AbstractThe bipartiteness of a graph is the minimum number of vertices whose deletion from G results in a bipartite graph. If a graph invariant decreases or increases with addition of edges of its complement, then it is called a monotonic graph invariant. In this article, we determine the extremal values of some famous monotonic graph invariants, and characterize the corresponding extremal graphs in the class of all connected graphs with a given vertex bipartiteness. 相似文献
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We determine the maximum values of the reverse Wiener indices of the unicyclic graphs with given cycle length, number of pendent
vertices and maximum degree, respectively, and characterize the extremal graphs. We also determine the unicyclic graphs of
given cycle length and diameter with minimum Wiener index.
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A unicyclic graph is a graph whose number of edges is equal to the number of vertices. Guo Shu-Guang [S.G. Guo, The largest Laplacian spectral radius of unicyclic graph, Appl. Math. J. Chinese Univ. Ser. A. 16 (2) (2001) 131–135] determined the first four largest Laplacian spectral radii together with the corresponding graphs among all unicyclic graphs on n vertices. In this paper, we extend this ordering by determining the fifth to the ninth largest Laplacian spectral radii together with the corresponding graphs among all unicyclic graphs on n vertices. 相似文献
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Let G =(V, E) be a simple connected graph with n(n ≥ 3) vertices and m edges,with vertex degree sequence {d1, d2,..., dn}. The augmented Zagreb index is defined as AZI =AZI(G)=∑ij∈E(didj/di+dj-2)3. Using the properties of inequality, we investigate the bounds of AZI for connected graphs, in particular unicyclic graphs in this paper, some useful conclusions are obtained. 相似文献