Spectra of Corona Based on the Total Graph

Authors

  • Xue-Qin Zhu College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, Zhejiang, P.R. China
  • Gui-Xian Tian College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, Zhejiang, P.R. China
  • Shu-Yu Cui Xingzhi College, Zhejiang Normal University, Jinhua 321004, Zhejiang, P.R. China

DOI:

https://doi.org/10.4208/jms.v49n1.16.09

Keywords:

Adjacency matrix, Laplacian matrix, signless Laplacian matrix, spectrum, total corona.

Abstract

For two simple connected graphs $G_1$ and $G_2$, we introduce a new graph operation called the total corona $G_1⊛G_2$ on $G_1$ and $G_2$ involving the total graph of $G_1.$ Subsequently, the adjacency (respectively, Laplacian and signless Laplacian) spectra of $G_1⊛G_2$ are determined in terms of these of a regular graph $G_1$ and an arbitrary graph $G_2.$ As applications, we construct infinitely many pairs of adjacency (respectively, Laplacian and signless Laplacian) cospectral graphs. Besides we also compute the number of spanning trees of $G_1⊛G_2.$

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Published

2018-08-16

Issue

Vol. 49 No. 1 (2016)

Section

Articles