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

Document Type : Original paper

Authors

1 Department of Mathematics, College of Engineering and Technology, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chengalpet 603 203, India

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

Abstract

Let dx be the degree of the vertex x in a graph G. The Randić index of G is defined by R(G)=xyE(G)(dxdy)12. 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.

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