Spectra of Corona Based on the Total Graph

Spectra of Corona Based on the Total Graph

Year:    2016

Author:    Xue-Qin Zhu, Gui-Xian Tian, Shu-Yu Cui

Journal of Mathematical Study, Vol. 49 (2016), Iss. 1 : pp. 72–81

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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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

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

Journal of Mathematical Study, Vol. 49 (2016), Iss. 1 : pp. 72–81

Published online:    2016-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    Adjacency matrix Laplacian matrix signless Laplacian matrix spectrum total corona.

Author Details

Xue-Qin Zhu

Gui-Xian Tian

Shu-Yu Cui

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