Harmonic Index and Randic Index of Generalized Transformation Graphs

Harishchandra S. Ramane, B. Basavanagoud, Raju B. Jummannaver

Abstract


The harmonic index of a graph $G$ is defined as the sum of weights $\frac{2}{d_G(u)+d_G(v)}$ of all edges $uv$ of $G$ and the Randi\'{c} index of a graph $G$ is defined as the sum of weights $\frac{1}{\sqrt{d_G(u)d_G(v)}}$ of all edges $uv$ of $G$, where $d_G(u)$ is the degree of a vertex $u$ in $G$. In this paper, the expressions for the harmonic index and Randi\'{c} index of the generalized transformation graphs $G^{xy}$ and for their complement graphs are obtained in terms of the parameters of underline graphs.

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