نتایج جستجو برای: unicyclic graph

تعداد نتایج: 198174  

2008
Domingos M. Cardoso Peter Rowlinson Slobodan K. Simić

We prove that the minimum value of the least eigenvalue of the signless Laplacian of a connected nonbipartite graph with a prescribed number of vertices is attained solely in the unicyclic graph obtained from a triangle by attaching a path at one of its endvertices. © 2008 Elsevier Inc. All rights reserved. AMS classification: 05C50

2012
XIAOLING SHEN YAOPING HOU

Let Gr,p be a graph obtained from a path by adjoining a cycle Cr of length r to one end and the central vertex of a star Sp on p vertices to the other end. In this paper, it is proven that unicyclic graph Gr,p with r even is determined by its Laplacian spectrum except for n = p+4.

Journal: :Eur. J. Comb. 2010
Yarong Wu Jinlong Shu

Let G be a simple connected graph with n vertices and n edges which we call an unicyclic graph. In this paper, we first investigate the least eigenvalue λn(G), then we present two sharp bounds of the spread s(G) of G. AMS classification: 05C50 ,05C35

Journal: :bulletin of the iranian mathematical society 2013
z. du b. zhou

the reverse degree distance of a connected graph $g$ is defined in discrete mathematical chemistry as [ r (g)=2(n-1)md-sum_{uin v(g)}d_g(u)d_g(u), ] where $n$, $m$ and $d$ are the number of vertices, the number of edges and the diameter of $g$, respectively, $d_g(u)$ is the degree of vertex $u$, $d_g(u)$ is the sum of distance between vertex $u$ and all other vertices of $g$, and $v(g)$ is the ...

2014
Lihua YOU Xin DONG

The Balaban index of a connected graph G is defined as J(G) = |E(G)| μ+ 1 ∑ e=uv∈E(G) 1 √ DG(u)DG(v) , and the Sum-Balaban index is defined as SJ(G) = |E(G)| μ+ 1 ∑ e=uv∈E(G) 1 √ DG(u)+DG(v) , where DG(u) = ∑ w∈V (G) dG(u,w), and μ is the cyclomatic number of G. In this paper, the unicyclic graphs with the maximum Balaban index and the maximum Sum-Balaban index among all unicyclic graphs on n v...

2002
Yaoping Hou Ivan Gutman Ching-Wah Woo

Let G be a graph on n vertices and let λ1, λ2, . . . , λn be its eigenvalues. The energy of G is defined as E(G) = |λ1| + |λ2| + · · · + |λn|. For various classes of unicyclic graphs, the graphs with maximal energy are determined. Let P 6 n be obtained by connecting a vertex of the circuit C6 with a terminal vertex of the path Pn−6. For n 7, P 6 n has the maximal energy among all connected unic...

Journal: :Mathematical and Computer Modelling 2011
Rundan Xing Bo Zhou

The hyper-Kirchhoff index is introduced when the hyper-Wiener operator is applied to the resistance-distance matrix of a connected graph. We give lower and upper bounds for the hyper-Kirchhoff index, and determine the n-vertex unicyclic graphs with the smallest, the second and the third smallest as well as the largest, the second and the third largest hyper-Kirchhoff indices for n ≥ 5. We also ...

Journal: :Ars Comb. 2012
Dongdong Wang Hongbo Hua

The energy of a graph is defined as the sum of the absolute values of all the eigenvalues of the graph. In the paper, we characterize the graphs with minimal energy in the class of bipartite unicyclic graphs of a given (p, q)–bipartition, where q ≥ p ≥ 2.

Journal: :Electronic Notes in Discrete Mathematics 2004
William Y. C. Chen Xueliang Li Chao Wang Xiaoyan Zhang

In this paper, we give graph-theoretic algorithms of linear time to the Minimum All-Ones Problem for unicyclic and bicyclic graphs. These algorithms are based on a graph-theoretic algorithm of linear time to the Minimum All-Ones Problem with Restrictions for trees.

2007
Leslie Hogben

Orthogonal representations are used to show that complements of certain sparse graphs have (positive semidefinite) minimum rank at most 4. This bound applies to the complement of a 2-tree and to the complement of a unicyclic graph. Hence for such graphs, the sum of the minimum rank of the graph and the minimum rank of its complement is at most two more than the order of the graph. The minimum r...

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