More on energy and Randic energy of specific graphs

Abstract

Let $G$ be a simple graph of order $n$. The energy $E(G)$ of the graph $G$ is the sum of the absolute values of the eigenvalues of $G$. The Randić matrix of $G$, denoted by $R(G)$, is defined as the $n\times n$ matrix whose $(i,j)$-entry is $(d_i{d}_j{)}^{\frac{-1}{2}}$ if $v_i$ and $v_j$ are adjacent and $0$ for another cases. The Randić energy $RE$ of $G$ is the sum of absolute values of the eigenvalues of $R(G)$. In this paper we compute the energy and Randić energy for certain graphs. Also we propose a conjecture on Randić energy.

14 pages