On Randic, Seidel, and Laplacian Energy of NEPS Graph

Abstract

Let Z be the simple graph; then, we can obtain the energy EZ of a graph Z by taking the absolute sum of the eigenvalues of the adjacency matrix of Z. In this research, we have computed different energy invariants of the noncompleted extended P-Sum (NEPS) of graph Zi. In particular, we investigate the Randic, Seidel, and Laplacian energies of the NEPS of path graph Pni with any base ℬ. Here, n denotes the number of vertices and i denotes the number of copies of path graph Pn. Some of the results depend on the number of zeroes in base elements, for which we use the notation j.