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

Xue-Qin Zhu, Gui-Xian Tian & Shu-Yu Cui

DOI: 10.4208/jms.v49n1.16.09

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.

  • AMS Subject Headings

05C50, 05C90

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

1023982804@qq.com (Xue-Qin Zhu)

gxtian@zjnu.cn (Gui-Xian Tian)

cuishuyu@163.com (Shu-Yu Cui)

  • BibTex
  • RIS
  • TXT
@Article{JMS-49-72, author = {Zhu , Xue-QinTian , Gui-Xian and Cui , Shu-Yu}, 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 $G_1⊛G_2.$

Zhu , Xue-QinTian , Gui-Xian and Cui , Shu-Yu. (2016). 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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