General Randić index of unicyclic graphs with given maximum degree

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Document Type : Original paper

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Department of Mathematics and Applied Mathematics, University of the Free State, Bloemfontein, South Africa

Abstract

The general Randi'{c} index of a graph G is defined as Ra(G)=∑uv∈E(G)[dG(u)dG(v)]a, where a∈R, E(G) is the set of edges of G, and dG(u) and dG(v) are the degrees of vertices u and v, respectively. Among unicyclic graphs with given number of vertices and maximum degree, we present the graph with the largest value of Ra for a<0, and graphs having the smallest values of Ra for a>0.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 17 May 2025

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