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

References

• [1] G. Chinta, J. Jorgenson, A. Karlsson, Zeta functions, heat kernels and spectral asymptotic on degenerating families of discrete tori, Nagoya Math. J., 198 (2010), 121--172
  • View Article
  • MathSciNet
  • Google Scholar


• [2] D. M. Cvetković, Applications of graph spectra: An introduction to the literature, Zb. Rad. (Beogr.), 13 (2009), 7--31
  • View Article
  • MathSciNet
  • MATH


• [3] K. C. Das, I. Gutman, A. S. Cevik, B. Zhou, On Laplacian energy, MATCH Commun. Math. Comput. Chem., 70 (2013), 689--696
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] K. C. Das, S. A. Mojalal, On energy and Laplacian energy of graphs, Electron. J. Linear Algebra, 31 (2016), 167--186
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] A. R. Fiuj Laali, H. Haj Seyyed Javadi, Spectra of some special bipartite graphs, Miskolc Math. Notes, 18 (2017), 295--305
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [6] S. Rahimi Sharbaf, F. Fayazi, Laplacian energy of a fuzzy graph, Iran. J. Math. Chem., 5 (2014), 1--10
  • View Article
  • Google Scholar
  • MATH


• [7] K. G. Sreekumar, Two-S-Three transformation function and its properties, Int. J. Math. Arch., 9 (2018), 83--88
  • View Article


• [8] K. G. Sreekumar, K. Manilal, $n^{th}$ SM Sum graphs and Some parameters, Int. J. Math. Anal., 11 (2017), 105--113
  • View Article
  • Google Scholar


• [9] K. G. Sreekumar, K. Manilal, Hosoya polynomial and Harary index of SM family of graphs, J. Inf. Optim. Sci., 39 (2018), 581--590
  • View Article
  • MathSciNet
  • Google Scholar


• [10] K. G. Sreekumar, K. Manilal, Automorphism groups of weakly semi regular bipartite graphs, Int. J. Sci. Tech. Res., 8 (2019), 728--732
  • View Article


• [11] B. Zhou, Energy of a graph, MATCH Commun. Math. Comput. Chem., 51 (2004), 111--118
  • View Article