Spectra of Corona Based on the Total Graph (Journal of Mathematical Study, 2018)
For two simple connected graphs $G_1$ and $G_2$, we introduce a new graph operationcalled 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) spectraof $G_1⊛G_2$ are determined in terms of these of a regular graph $G_1$ and an arbitrarygraph $G_2.$ As applications, we construct infinitely many pairs of adjacency (respectively,Laplacian and signless Laplacian) cospectral graphs. Besides we also computethe number of spanning trees of $G_1⊛G_2.$
Keywords: Adjacency matrix; Laplacian matrix; signless Laplacian matrix; spectrum; total corona.