The star is the tree with greatest greatest Laplacian eigenvalue
Ivan Gutman (2002)
Kragujevac Journal of Mathematics
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Ivan Gutman (2002)
Kragujevac Journal of Mathematics
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D. Cvetković (2008)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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Kouider, Mekkia, Vestergaard, Preben Dahl (2006)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Ji-Ming Guo, Lin Feng, Jiong-Ming Zhang (2010)
Czechoslovak Mathematical Journal
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In this paper we investigate the effect on the multiplicity of Laplacian eigenvalues of two disjoint connected graphs when adding an edge between them. As an application of the result, the multiplicity of 1 as a Laplacian eigenvalue of trees is also considered.
Sebastian M. Cioabă, Xiaofeng Gu (2016)
Czechoslovak Mathematical Journal
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The eigenvalues of graphs are related to many of its combinatorial properties. In his fundamental work, Fiedler showed the close connections between the Laplacian eigenvalues and eigenvectors of a graph and its vertex-connectivity and edge-connectivity. We present some new results describing the connections between the spectrum of a regular graph and other combinatorial parameters such as its generalized connectivity, toughness, and the existence of spanning trees with bounded degree. ...
Yilun Shang (2016)
Open Mathematics
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As a generalization of the Sierpiński-like graphs, the subdivided-line graph Г(G) of a simple connected graph G is defined to be the line graph of the barycentric subdivision of G. In this paper we obtain a closed-form formula for the enumeration of spanning trees in Г(G), employing the theory of electrical networks. We present bounds for the largest and second smallest Laplacian eigenvalues of Г(G) in terms of the maximum degree, the number of edges, and the first Zagreb index of G....
Damir Vukičević, Ivan Gutman (2004)
Kragujevac Journal of Mathematics
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Gutman, I. (2003)
Bulletin. Classe des Sciences Mathématiques et Naturelles. Sciences Mathématiques
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Mustapha Aouchiche, Pierre Hansen (2014)
Czechoslovak Mathematical Journal
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The distance Laplacian of a connected graph is defined by , where is the distance matrix of , and is the diagonal matrix whose main entries are the vertex transmissions in . The spectrum of is called the distance Laplacian spectrum of . 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...