On the Energy of Certain Recursive Structures

Abstract

Eigenvalues of a graph are the eigenvalues of its adjacency matrix. The multiset of eigenvalues is called the $spectrum$. The energy of a graph is defined as the sum of the absolute values of its eigenvalues. In this paper, we devise an algorithm that generates the adjacency matrix of $WK$-recursive structures $WK(3,L)$ and $WK(4,L)$, and use it to effectively compute the spectrum and energy of these graphs.