Author
Somnath Paul
Bio: Somnath Paul is an academic researcher from Tezpur University. The author has contributed to research in topics: Distance matrix & Spectral radius. The author has an hindex of 8, co-authored 19 publications receiving 223 citations.
Papers
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TL;DR: In this paper, the authors considered the class of all connected graphs of order n with r pendent vertices and determined the unique graph with minimal distance spectral radius in G n r.
42 citations
TL;DR: In this paper, it was shown that the largest distance Laplacian eigenvalue of a path is simple and the corresponding eigenvector has the similar property like that of a Fiedler vector.
41 citations
TL;DR: In this paper, the authors determine the unique graph with minimum distance spectral radius among all connected bipartite graphs of order n with a given matching number, where n is the number of vertices in the graph.
37 citations
TL;DR: In this paper, it was shown that the dumbbell is the unique tree that maximizes the distance spectral radius of trees on n vertices and matching number m, which was conjectured by Aleksandar Ilic.
Abstract: In this article, we prove that among trees on n vertices and matching number m, the dumbbell is the unique tree that maximizes the distance spectral radius, which was conjectured by Aleksandar Ilic [Distance spectral radius of trees with given matching number, Discr. Appl. Math. 158 (2010), pp. 1799–1806]. In addition, we find the unique tree that maximizes the distance spectral radius in the class of trees with a given number of pendent vertices.
35 citations
TL;DR: In this article, the unique graph with maximal distance spectral radius in the class of graphs without a pendent vertex was determined, where the spectral radius of the graph is the same as that of the vertex.
19 citations
Cited by
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01 Jan 2009
TL;DR: In this article, the authors introduce the concept of graph operations and modifications, and characterizations of spectra by characterizations by spectra and one eigenvalue, and Laplacians.
Abstract: Preface 1. Introduction 2. Graph operations and modifications 3. Spectrum and structure 4. Characterizations by spectra 5. Structure and one eigenvalue 6. Spectral techniques 7. Laplacians 8. Additional topics 9. Applications Appendix Bibliography Index of symbols Index.
398 citations
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TL;DR: In this paper, the adjacency matrix, a matrix of O's and l's, is used to store a graph or digraph in a computer, and certain matrix operations are seen to correspond to digraph concepts.
Abstract: In order to store a graph or digraph in a computer, we need something other than the diagram or the formal definition. This something is the adjacency matrix, a matrix of O’s and l’s. The l’s correspond to the arcs of the digraph. Certain matrix operations will be seen to correspond to digraph concepts.
292 citations
TL;DR: The present paper reports on the results related to the distance matrix of a graph and its spectral properties.
233 citations
01 Jan 2016
TL;DR: An introduction to the theory of graph spectra is available in the book collection an online access to it is set as public so you can download it instantly and is universally compatible with any devices to read.
Abstract: an introduction to the theory of graph spectra is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the an introduction to the theory of graph spectra is universally compatible with any devices to read.
222 citations
01 Nov 2013
TL;DR: In this paper, the spectral properties of the distance matrix of a connected graph and its spectral properties were investigated and the authors reported the results related to the distance matrices of a graph and their spectral properties.
Abstract: In 1971, Graham and Pollack established a relationship between the number of negative eigenvalues of the distance matrix and the addressing problem in data communication systems. They also proved that the determinant of the distance matrix of a tree is a function of the number of vertices only. Since then several mathematicians were interested in studying the spectral properties of the distance matrix of a connected graph. Computing the distance characteristic polynomial and its coefficients was the first research subject of interest. Thereafter, the eigenvalues attracted much more attention. In the present paper, we report on the results related to the distance matrix of a graph and its spectral properties.
212 citations