摘要：The general Randić matrix of a graph $G$, denoted by $GR(G)$ is an $n \times n$ matrix whose $(i, j)$-th entry is $(d_i d_j)^\alpha$, $\alpha \in \Bbb{R}$ if the vertices $v_i$ and $v_j$ are adjacent and $0$ otherwise, where $d_i$ is the degree of a vertex $v_i$ and $n$ is the order of $G$. The general Randić energy $E_{GR}(G)$ of $G$ is the sum of the absolute values of the eigenvalues of $GR(G)$. In this paper, we compute the general Randić polynomial and the general Randić energy of path, cycle, complete graph, complete bipartite graph, friendship graph and Dutch windmill graph.
关键词：General Randić eigenvalues; general Randić energy; Randić index; degree of a vertex.
