The Generalized Distance Spectrum of the Join of Graphs

Abdollah Alhevaz, Maryam Baghipur, Hilal Ahmad, Yilun Shang

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
78 Downloads (Pure)

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.
Original languageEnglish
Article number169
JournalSymmetry
Volume12
Issue number1
DOIs
Publication statusPublished - 15 Jan 2020

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