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
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