General Sombor index: a study of branching in trees and solution for maximal trees with prescribed maximum degree
Sultan Ahmad () and
Kinkar Chandra Das ()
Additional contact information
Sultan Ahmad: National University of Sciences and Technology
Kinkar Chandra Das: Sungkyunkwan University
Journal of Combinatorial Optimization, 2025, vol. 50, issue 2, No 9, 23 pages
Abstract:
Abstract The general Sombor ( $$\mathcal{S}\mathcal{O}_\alpha $$ ) index of a graph G is defined as the sum of weights $$\Big (d^2_x(G) +d^2_y(G)\Big )^\alpha $$ over all edges xy of G, where $$\alpha \ne 0$$ is a real number and $$d_x(G)$$ denotes the degree of a vertex x in G. In this paper, we focus on two specific classes of trees: $${{\mathcal {T}}}_{n,b}$$ , the set of all n-vertex trees with b branching vertices, and $${{\mathcal {T}}}_{n,\Delta }$$ , the set of all n-vertex trees with prescribed maximum degree $$\Delta $$ . Thus the purpose of this paper is twofold concerning the $$\mathcal{S}\mathcal{O}_\alpha $$ index: (i) to characterize the minimal trees in $${{\mathcal {T}}}_{n,b}$$ when $$\alpha > 0$$ , and (ii) to characterize the maximal trees in $${{\mathcal {T}}}_{n,\Delta }$$ when $$0
Keywords: General Sombor index; Extremal trees; Branching vertex; Maximum degree; 05C09; 05C35; 05C92 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:
Downloads: (external link)
http://link.springer.com/10.1007/s10878-025-01343-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:50:y:2025:i:2:d:10.1007_s10878-025-01343-x
Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878
DOI: 10.1007/s10878-025-01343-x
Access Statistics for this article
Journal of Combinatorial Optimization is currently edited by Thai, My T.
More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().