Universal Distance Spectra of Join of Graphs

Authors

  • Sakthidevi Kaliyaperumal Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai
  • Kalyani Desikan Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, India

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i1.5019

Keywords:

Universal distance spectrum, Seidal matrix, Joined Union, Complete split graph

Abstract

Consider G a simple connected graph. In this paper, we introduce the Universal distance matrix UD (G). For α, β, γ, δ ∈ R and β ̸= 0, the universal distance matrix UD (G) is defined as
UD (G) = αTr (G) + βD(G) + γJ + δI,
where Tr (G) is the diagonal matrix whose elements are the vertex transmissions, and D(G) is the distance matrix of G. Here J is the all-ones matrix, and I is the identity matrix. In this paper, we obtain the universal distance spectra of regular graph, join of two regular graphs, joined union of three regular graphs, generalized joined union of n disjoint graphs with one arbitrary graph H. As a consequence, we obtain the eigenvalues of distance matrix, distance Laplacian matrix, distance signless Laplacian matrix, generalized distance matrix, distance Seidal matrix and distance matrices of complementary graphs.

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Published

2024-01-31

Issue

Section

Nonlinear Analysis

How to Cite

Universal Distance Spectra of Join of Graphs. (2024). European Journal of Pure and Applied Mathematics, 17(1), 462-476. https://doi.org/10.29020/nybg.ejpam.v17i1.5019

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