Displaying similar documents to “Spectral study of alliances in graphs”

The Minimum Spectral Radius of Signless Laplacian of Graphs with a Given Clique Number

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.

A sharp upper bound for the spectral radius of a nonnegative matrix and applications

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.

The Laplacian spectral radius of graphs

Jianxi Li, Wai Chee Shiu, An Chang (2010)

Czechoslovak Mathematical Journal

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The Laplacian spectral radius of a graph is the largest eigenvalue of the associated Laplacian matrix. In this paper, we improve Shi's upper bound for the Laplacian spectral radius of irregular graphs and present some new bounds for the Laplacian spectral radius of some classes of graphs.

Extremal inverse eigenvalue problem for matrices described by a connected unicyclic graph

Bijoya Bardhan, Mausumi Sen, Debashish Sharma (2024)

Applications of Mathematics

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In this paper, we deal with the construction of symmetric matrix whose corresponding graph is connected and unicyclic using some pre-assigned spectral data. Spectral data for the problem consist of the smallest and the largest eigenvalues of each leading principal submatrices. Inverse eigenvalue problem (IEP) with this set of spectral data is generally known as the extremal IEP. We use a standard scheme of labeling the vertices of the graph, which helps in getting a simple relation between...