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Yi-Zheng Fan, Song Wu (2008)
Discussiones Mathematicae Graph Theory
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The spectral radius of a graph is defined by that of its unoriented Laplacian matrix. In this paper, we determine the unicyclic graphs respectively with the third and the fourth largest spectral radius among all unicyclic graphs of given order.
Lin Cui, Yi-Zheng Fan (2010)
Discussiones Mathematicae Graph Theory
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In this paper, we determine the graph with maximal signless Laplacian spectral radius among all connected graphs with fixed order and given number of cut vertices.
Juan Alberto Rodríguez-Velazquez, Jose Maria Sigarreta Almira (2007)
Discussiones Mathematicae Graph Theory
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In this paper we obtain several tight bounds on different types of alliance numbers of a graph, namely (global) defensive alliance number, global offensive alliance number and global dual alliance number. In particular, we investigate the relationship between the alliance numbers of a graph and its algebraic connectivity, its spectral radius, and its Laplacian spectral radius.
Lihua You, Yujie Shu, Xiao-Dong Zhang (2016)
Czechoslovak Mathematical Journal
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We obtain a sharp upper bound for the spectral radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency spectral radius, the Laplacian spectral radius, the signless Laplacian spectral radius, the distance spectral radius, the distance Laplacian spectral radius, the distance signless Laplacian spectral radius of an undirected graph or a digraph. These results are new or generalize some known results.
Dragoš Cvetković (2012)
The Yugoslav Journal of Operations Research
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Lihua Feng, Guihai Yu (2009)
Publications de l'Institut Mathématique
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Li Su, Hong-Hai Li, Jing Zhang (2014)
Discussiones Mathematicae Graph Theory
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In this paper we observe that the minimal signless Laplacian spectral radius is obtained uniquely at the kite graph PKn−ω,ω among all connected graphs with n vertices and clique number ω. In addition, we show that the spectral radius μ of PKm,ω (m ≥ 1) satisfies [...] More precisely, for m > 1, μ satisfies the equation [...] where [...] and [...] . At last the spectral radius μ(PK∞,ω) of the infinite graph PK∞,ω is also discussed.
Richard A. Brualdi, Ernie S. Solheid (1986)
Publications de l'Institut Mathématique
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D. M. Cvetković, I. Gutman (1975)
Publications de l'Institut Mathématique
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Marianna Bolla, Ahmed Elbanna (2016)
Special Matrices
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We will discuss how graph based matrices are capable to find classification of the graph vertices with small within- and between-cluster discrepancies. The structural eigenvalues together with the corresponding spectral subspaces of the normalized modularity matrix are used to find a block-structure in the graph. The notions are extended to rectangular arrays of nonnegative entries and to directed graphs. We also investigate relations between spectral properties, multiway discrepancies,...
Mostafa Mbekhta, Jaroslav Zemánek (2007)
Banach Center Publications
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