Authors: Damnjanovic, Ivan
Stevanović, Dragan 
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: AN ALTERNATIVE PROOF OF THE SOMBOR INDEX MINIMIZING PROPERTY OF GREEDY TREES
Journal: Publications de l'Institut Mathematique
Volume: 113
Issue: 127
First page: 57
Last page: 65
Issue Date: 2023
Rank: M24
ISSN: 0350-1302
DOI: 10.2298/PIM2327057D
Abstract: 
Recently, Gutman defined a new graph invariant which is named the Sombor index SO(G) of a graph G and is computed via the expression (Formula Presented) where deg(u) represents the degree of the vertex u in G and the summing is performed across all the unordered pairs of adjacent vertices u and v. Damnjanović et al. have implemented an earlier result obtained by Wang in order to show that, among all the trees TD that have a specified degree sequence D, the greedy tree must attain the minimum Sombor index. Here we provide an alternative proof of this same result by constructing an auxiliary graph invariant named the pseudo-Sombor index and without relying on any other earlier results.
Keywords: degree sequence | greedy tree | Sombor index | trees
Publisher: Mathematical Institute of the Serbian Academy of Sciences and Arts

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