| 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 $G_1⊛G_2.$ |
