Note on the Randic Energy of Graphs

Jun He, Yan-Min Liu, Jun-Kang Tian

If $G$ is a graph on $n$ vertices, and $d_i$ is the degree of its $i$-th vertex, then the Randic matrix of $G$ is the square matrix of order $n$ whose $(i, j)$-entry is equal to $1/\sqrt{d_id_j}$ if the $i$-th and $j$-th vertex of $G$ are adjacent, and zero otherwise. In this note, we obtain some new lower and upper bounds for the Randic energy.