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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 $G_1⊛G_2.$

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v49n1.16.09}, url = {http://global-sci.org/intro/article_detail/jms/991.html} }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 $G_1⊛G_2.$

*Journal of Mathematical Study*.

*49*(1). 72-81. doi:10.4208/jms.v49n1.16.09