Degree-weighted Sombor indices of trees and unicyclic graphs: An extremal approach

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Document Type : Original paper

Authors

1 Department of Mathematics and Computer Science, Sirjan University of Technology, Sirjan, Iran

2 University of Zagreb, Faculty of Civil Engineering, Zagreb, Croatia

Abstract

‎We consider two generalizations of the Sombor index, obtained by weighting the standard contribution dΩ(η)2+dΩ(η′)2 of an edge ηη′ of a graph Ω by the sum and by the product of degrees of its end-vertices, respectively. The first generalization has been considered under the name of the elliptic Sombor index, while the second one seems to be new. We consider trees and unicyclic graphs on a given number of vertices n with a given maximum degree Δ and characterize the graphs minimizing both generalizations over those classes of graphs.

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References

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Communications in Combinatorics and Optimization

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Available Online from 12 May 2025

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