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 G1⋆G2. Let S(G) be the subdivision graph of G. The SSG-vertex join G1⋆G2 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 G1⋆G2. As applications, we construct many pairs of normalized Laplacian cospectral graphs, the normalized Laplacian energy, and the degree Kirchhoff index of G1⋆G2.
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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.