Displaying similar documents to “Algebraic conditions for t -tough graphs”

On graphs with the largest Laplacian index

Bo Lian Liu, Zhibo Chen, Muhuo Liu (2008)

Czechoslovak Mathematical Journal

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Let G be a connected simple graph on n vertices. The Laplacian index of G , namely, the greatest Laplacian eigenvalue of G , is well known to be bounded above by n . In this paper, we give structural characterizations for graphs G with the largest Laplacian index n . Regular graphs, Hamiltonian graphs and planar graphs with the largest Laplacian index are investigated. We present a necessary and sufficient condition on n and k for the existence of a k -regular graph G of order n with the...

Some properties of the distance Laplacian eigenvalues of a graph

Mustapha Aouchiche, Pierre Hansen (2014)

Czechoslovak Mathematical Journal

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The distance Laplacian of a connected graph G is defined by ℒ = Diag ( Tr ) - 𝒟 , where 𝒟 is the distance matrix of G , and Diag ( Tr ) is the diagonal matrix whose main entries are the vertex transmissions in G . The spectrum of ℒ is called the distance Laplacian spectrum of G . In the present paper, we investigate some particular distance Laplacian eigenvalues. Among other results, we show that the complete graph is the unique graph with only two distinct distance Laplacian eigenvalues. We establish some properties...

Spectral characterization of multicone graphs

Jianfeng Wang, Haixing Zhao, Qiongxiang Huang (2012)

Czechoslovak Mathematical Journal

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A multicone graph is defined to be the join of a clique and a regular graph. Based on Zhou and Cho's result [B. Zhou, H. H. Cho, Remarks on spectral radius and Laplacian eigenvalues of a graph, Czech. Math. J. 55 (130) (2005), 781–790], the spectral characterization of multicone graphs is investigated. Particularly, we determine a necessary and sufficient condition for two multicone graphs to be cospectral graphs and investigate the structures of graphs cospectral to a multicone graph....