Faculty Publications

A Note On Generalized Semitotal Point Graphs

Document Type

Article

Keywords

Characteristic polynomials, Degree Kirchhoff index, Ihara zeta function, Kirchhoff index, Weighted Kirchhoff index

Journal/Book/Conference Title

Discrete Applied Mathematics

Volume

293

First Page

114

Last Page

127

Abstract

Let Rsk(G) be the graph obtained from a graph G by gluing k distinct path graphs Ps+2 to both vertices incident to each edge of G. In this paper, we derive a factorization formula for the generalized characteristic polynomial of the graph Rsk(G), where G is regular. As particular cases, we obtain formulas for the characteristic polynomials of the adjacency, Laplacian, normalized Laplacian, and signless Laplacian matrices of Rsk(G), as well as for the Ihara zeta function of Rsk(G), where G is regular. We also derive formulas for the Kirchhoff, additive degree-Kirchhoff, and multiplicative degree-Kirchhoff indices of Rsk(G), where G is regular. In addition, we determine the weighted Kirchhoff index of Rsk(G), for an arbitrary graph G. This work generalizes recent results on semitotal point graphs.

Department

Department of Mathematics

Original Publication Date

4-15-2021

DOI of published version

10.1016/j.dam.2021.01.009

Repository

UNI ScholarWorks, Rod Library, University of Northern Iowa

Language

en

Link to Full Text

Comments?

Share

COinS