On the ordering of the Randić index of unicyclic and bicyclic graphs

Document Type : Original paper


1 Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology

2 Department of Mathematics, School of Arts, Sciences and Humanities, SASTRA Deemed University, Thanjavur, India


Let $d_x$ be the degree of the vertex $x$ in a graph $G$. The Randić index of $G$ is defined by $R(G) = \sum_{xy \in E(G)} (d_x d_y)^ {-\frac{1}{2}}$. Recently, Hasni et al. [Unicyclic graphs with Maximum Randi'{c} indices, Communication in Combinatorics and Optimization, 1 (2023), 161--172] obtained the ninth to thirteenth maximum Randić indices among the unicyclic graphs with $n$ vertices. In this paper, we correct the ordering of Randić index of unicyclic graphs. In addition, we present the ordering of maximum Randi'c index among bicyclic graphs of order $n$.


Main Subjects

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