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On the Normalized Laplacian Spectrum of a New Join of Two Graphs

On the Normalized Laplacian Spectrum of a New Join of Two Graphs

Year:    2018

Author:    Xianzhang Wu, Lili Shen

Annals of Applied Mathematics, Vol. 34 (2018), Iss. 4 : pp. 407–415

Abstract

Given graphs G1 and G2, we define a graph operation on G1 and G2, namely the SSG-vertex join of G1 and G2, denoted by G1G2. Let S(G) be the subdivision graph of G. The SSG-vertex join G1G2 is the graph obtained from S(G1) and S(G2) by joining each vertex of G1 with each vertex of G2. In this paper, when Gi(i=1,2) is a regular graph, we determine the normalized Laplacian spectrum of G1G2. As applications, we construct many pairs of normalized Laplacian cospectral graphs, the normalized Laplacian energy, and the degree Kirchhoff index of G1G2.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2018-AAM-20588

Annals of Applied Mathematics, Vol. 34 (2018), Iss. 4 : pp. 407–415

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    9

Keywords:    spectrum SSG-vertex join normalized Laplacian cospectral graphs normalized Laplacian energy degree Kirchhoff index.

Author Details

Xianzhang Wu Email

Lili Shen Email