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 - <p style="text-align: justify;">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 $G_1⊛G_2.$</p>