Narrow Results

Let $G$ be a graph with $n$ vertices, and let $d_u$ be the degree of the vertex $u$ in the graph $G$. The Randić matrix of $G$ is the square matrix of order $n$ whose $(i,j)$-entry is equal to ${(d_u{d}_v)}^{\frac{-1}{2}}$ if the vertex $u$ and the vertex $v$ of $G$ are adjacent, and $0$ otherwise. The Randić eigenvalues of $G$ are the eigenvalues of its Randić matrix and the Randić energy of $G$ is the sum of the absolute values of its Randić eigenvalues. In this paper, we obtain some new results for the Randić eigenvalues and the Randić energy of a graph.