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Open Access Research Article

Extremal trees and their properties for Sigma index with fixed degree sequence

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pp. 1239–1248Vol. 29Issue 3March 2026DOI: 10.47974/JDMSC-2198 Crossmark XML
Received:
13 Feb 2024
Published Online:
06 Aug 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2198
Pages:
1239–1248

Abstract

For a simple graph A = (VA, EA) where VA and EA are the vertex set and the edge set, respectively, the Sigma index of A is defined as  s(A) = Sxy ∈ EA (hx – hy)2, where hx denotes the degree of x ∈ VA.  In order to minimize and maximize the Sigma index among all trees, the extremal trees with fixed degree sequence are described in this study. The properties of the extremal trees are identified. 

Keywords

Subject Classifications

05C3505C0905C07

References

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