Heat kernel and \(D_{n,r}\) decomposition of some families of weakly semi-regular bipartite graphs

Volume 21, Issue 1, pp 69--77 http://dx.doi.org/10.22436/jmcs.021.01.07

Publication Date: March 22, 2020 Submission Date: June 10, 2019 Revision Date: January 27, 2020 Accteptance Date: February 05, 2020

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Authors

K. Manilal - Department of Mathematics, University College, University of Kerala, Thiruvananthapuram, India. K. G. Sreekumar - Department of Mathematics, University College, University of Kerala, Thiruvananthapuram, India. John K. Rajan - Department of Mathematics, University College, University of Kerala, Thiruvananthapuram, India.

Abstract

This paper studies the characteristic polynomial of distance matrices and adjacency matrices of some families of weakly semi-regular bipartite graphs. The \(D_{n,r}\) decomposition is a decomposition of distance matrices and adjacency matrices of some families of graphs. The general distance matrices and adjacency matrices of these graphs are decomposed into a further simpler form. The spectra of these graphs are also analysed. The \(D_{n,r}\) decomposition of these graphs is done so that analysis of eigenvalues and related parameters are possible with this decomposition. The heat kernel of these graphs is analysed.

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Keywords

• Distance matrix
• adjacency matrix
• \(n^{\rm th}\) SM balancing graphs
• \(n^{\rm th}\) SM sum graphs
• energy and spectrum
• heat Kernel of graphs
• bipartite Kneser graphs

MSC

•  05C99
•  05C50

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