Spectral Recognition of Graphs
Dragoš Cvetković (2012)
The Yugoslav Journal of Operations Research
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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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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.
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.
Dragoš Cvetković, Slobodan K. Simić (2009)
Publications de l'Institut Mathématique
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Cvetković, D., Rowlinson, P. (1988)
Publications de l'Institut Mathématique. Nouvelle Série
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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.
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,...
Petrović, Miroslav M. (1983)
Publications de l'Institut Mathématique. Nouvelle Série
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Ying Liu (2013)
Discussiones Mathematicae - General Algebra and Applications
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Let G be a graph with n vertices and ν(G) be the matching number of G. The inertia of a graph G, In(G) = (n₊,n₋,n₀) is an integer triple specifying the numbers of positive, negative and zero eigenvalues of the adjacency matrix A(G), respectively. Let η(G) = n₀ denote the nullity of G (the multiplicity of the eigenvalue zero of G). It is well known that if G is a tree, then η(G) = n - 2ν(G). Guo et al. [Ji-Ming Guo, Weigen Yan and Yeong-Nan Yeh. On the nullity and the matching number...
D. Cvetković (2005)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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Cvetković, Dragoš, Simić, Slobodan (1993)
Publications de l'Institut Mathématique. Nouvelle Série
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