On some aspects of the generalized Petersen graph - V. Yegnanarayanan (Electronic Journal of Graph Theory and Applications (EJGTA), 2017)
Let $p \ge 3$ be a positive integer and let $k \in {1, 2, ..., p-1} \ \lfloor p/2 \rfloor$. The generalized Petersen graph GP(p,k) has its vertex and edge set as $V(GP(p, k)) = \{u_i : i \in Zp\} \cup \{u_i^′ : i \in Z_p\}$ and $E(GP(p, k)) = \{u_i u_{i+1} : i \in Z_p\} \cup \{u_i^′ u_{i+k}^′ \in Z_p\} \cup \{u_iu_i^′ : i \in Z_p\}$. In this paper we probe its spectrum and determine the Estrada index, Laplacian Estrada index, signless Laplacian Estrada index, normalized Laplacian Estrada index, and energy of a graph. While obtaining some interesting results, we also provide relevant background and problems.