Volume 49, Issue 1
Spectra of Corona Based on the Total Graph

J. Math. Study, 49 (2016), pp. 72-81.

Published online: 2016-03

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• 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 $G_1⊛G_2.$

• Keywords

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

05C50, 05C90

1023982804@qq.com (Xue-Qin Zhu)

gxtian@zjnu.cn (Gui-Xian Tian)

cuishuyu@163.com (Shu-Yu Cui)

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@Article{JMS-49-72, author = {Xue-Qin and Zhu and 1023982804@qq.com and 13311 and College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, Zhejiang, P.R. China and Xue-Qin Zhu and Gui-Xian and Tian and gxtian@zjnu.cn and 13312 and College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, Zhejiang, P.R. China and Gui-Xian Tian and Shu-Yu and Cui and cuishuyu@163.com and 13313 and Xingzhi College, Zhejiang Normal University, Jinhua 321004, Zhejiang, P.R. China and Shu-Yu Cui}, title = {Spectra of Corona Based on the Total Graph}, journal = {Journal of Mathematical Study}, year = {2016}, volume = {49}, number = {1}, pages = {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 $G_1⊛G_2.$

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v49n1.16.09}, url = {http://global-sci.org/intro/article_detail/jms/991.html} }
TY - JOUR T1 - Spectra of Corona Based on the Total Graph AU - Zhu , Xue-Qin AU - Tian , Gui-Xian AU - Cui , Shu-Yu JO - Journal of Mathematical Study VL - 1 SP - 72 EP - 81 PY - 2016 DA - 2016/03 SN - 49 DO - http://doi.org/10.4208/jms.v49n1.16.09 UR - https://global-sci.org/intro/article_detail/jms/991.html KW - Adjacency matrix, Laplacian matrix, signless Laplacian matrix, spectrum, total corona. AB -

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 $G_1⊛G_2.$

Xue-Qin Zhu, Gui-Xian Tian & Shu-Yu Cui. (2019). Spectra of Corona Based on the Total Graph. Journal of Mathematical Study. 49 (1). 72-81. doi:10.4208/jms.v49n1.16.09
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