The Generalized Distance Spectrum of the Join of Graphs

Alhevaz, Abdollah, Baghipur, Maryam, Ganie, Hilal A. and Shang, Yilun (2020) The Generalized Distance Spectrum of the Join of Graphs. Symmetry, 12 (1). p. 169. ISSN 2073-8994

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Official URL: https://doi.org/10.3390/sym12010169

Abstract

Let G be a simple connected graph. In this paper, we study the spectral properties of the generalized distance matrix of graphs, the convex combination of the symmetric distance matrix D(G) and diagonal matrix of the vertex transmissions Tr(G) . We determine the spectrum of the join of two graphs and of the join of a regular graph with another graph, which is the union of two different regular graphs. Moreover, thanks to the symmetry of the matrices involved, we study the generalized distance spectrum of the graphs obtained by generalization of the join graph operation through their eigenvalues of adjacency matrices and some auxiliary matrices.

Item Type: Article
Uncontrolled Keywords: generalized distance matrix (spectrum); distance signless Laplacian matrix; joined union; lexicographic product; complete split graph; graph operation
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User: Elena Carlaw
Date Deposited: 18 Feb 2020 10:47
Last Modified: 18 Feb 2020 11:00
URI: http://nrl.northumbria.ac.uk/id/eprint/42111

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