Faculty Publications

On A Construction Using Commuting Regular Graphs

Document Type

Article

Keywords

Characteristic polynomial, Complexity, Ihara zeta function, Kirchhoff index, Middle graph, Quasitotal graph, Total graph

Journal/Book/Conference Title

Discrete Mathematics

Volume

340

Issue

3

First Page

532

Last Page

540

Abstract

We consider a construction using a pair of commuting regular graphs that generalizes the constructions of the middle, total, and quasitotal graphs. We derive formulae for the characteristic polynomials of the adjacency and Laplacian matrices and for the Ihara zeta function of the resulting graph. Using these formulae, we express the number of spanning trees and the Kirchhoff index of the resulting graph in terms of the Laplacian spectra of the two regular graphs used in the construction.

Department

Department of Mathematics

Original Publication Date

3-1-2017

DOI of published version

10.1016/j.disc.2016.07.018

Repository

UNI ScholarWorks, Rod Library, University of Northern Iowa

Language

en

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