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

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

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

Published online: 2016-03

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  • Abstract

For two simple connected graphs G1 and G2, we introduce a new graph operation called the total corona G1⊛G2 on G1 and G2 involving the total graph of G1. Subsequently, the adjacency (respectively, Laplacian and signless Laplacian) spectra of G1⊛G2 are determined in terms of these of a regular graph G1 and an arbitrary graph G2. 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 G1⊛G2.

  • 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-Qin and Tian , 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 G1 and G2, we introduce a new graph operation called the total corona G1⊛G2 on G1 and G2 involving the total graph of G1. Subsequently, the adjacency (respectively, Laplacian and signless Laplacian) spectra of G1⊛G2 are determined in terms of these of a regular graph G1 and an arbitrary graph G2. 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 G1⊛G2.

}, 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://dor.org/10.4208/jms.v49n1.16.09 UR - https://global-sci.org/intro/article_detail/jms/991.html KW - Adjacency matrix KW - Laplacian matrix KW - signless Laplacian matrix KW - spectrum KW - total corona AB -

For two simple connected graphs G1 and G2, we introduce a new graph operation called the total corona G1⊛G2 on G1 and G2 involving the total graph of G1. Subsequently, the adjacency (respectively, Laplacian and signless Laplacian) spectra of G1⊛G2 are determined in terms of these of a regular graph G1 and an arbitrary graph G2. 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 G1⊛G2.

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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