Maximum General Sum-Connectivity Index of Trees and Unicyclic Graphs with Given Order and Number of Pendant Vertices

Elize Swartz and Tomáš Vetrík ()
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Elize Swartz: Department of Mathematics and Applied Mathematics, University of the Free State, Bloemfontein 9301, South Africa
Tomáš Vetrík: Department of Mathematics and Applied Mathematics, University of the Free State, Bloemfontein 9301, South Africa

Mathematics, 2025, vol. 13, issue 19, 1-12

Abstract: For a ∈ R , the general sum-connectivity index of a graph G is defined as χ a ( G ) = ∑ u v ∈ E ( G ) [ d G ( u ) + d G ( v ) ] a , where E ( G ) is the set of edges of G and d G ( u ) and d G ( v ) are the degrees of vertices u and v , respectively. For trees and unicyclic graphs with given order and number of pendant vertices, we present upper bounds on the general sum-connectivity index χ a , where 0 < a < 1 . We also present the trees and unicyclic graphs that attain the maximum general sum-connectivity index for 0 < a < 1 .

Keywords: general sum-connectivity index; tree; unicyclic graph; pendant vertex (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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