Displaying similar documents to “Spectral integral variation of trees”

A result related to the largest eigenvalue of a tree

Gurusamy Rengasamy Vijayakumar (2008)

Discussiones Mathematicae Graph Theory

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In this note we prove that {0,1,√2,√3,2} is the set of all real numbers l such that the following holds: every tree having an eigenvalue which is larger than l has a subtree whose largest eigenvalue is l.

Connectivity, toughness, spanning trees of bounded degree, and the spectrum of regular graphs

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. ...

Small integral trees.

Brouwer, A.E. (2008)

The Electronic Journal of Combinatorics [electronic only]

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A note on distance spectral radius of trees

Yanna Wang, Rundan Xing, Bo Zhou, Fengming Dong (2017)

Special Matrices

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The distance spectral radius of a connected graph is the largest eigenvalue of its distance matrix. We determine the unique non-starlike non-caterpillar tree with maximal distance spectral radius.