**Authors:** Harishchandra S. Ramane, Gouramma A. Gudodagi

**Keywords:** General Randić eigenvalues, general Randić energy, Randić index, degree of a vertex.

### Abstract

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.

Harishchandra S. Ramane

Department of Mathematics,

Karnatak University,

Dharwad - 580003, India

Phone:+919945031752

E-mail:

Gouramma A. Gudodagi

Department of Mathematics,

KLE’s G. I. Bagewadi Arts, Science and Commerce College,

Nipani – 591237, India

Phone:+918095319099

E-mail:

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