What question did this study set out to answer?

This survey aims to compile existing extremal results and bounds related to elliptic Sombor and Euler-Sombor indices.

June 15, 2026Open Access

Survey on Extremal Results and Bounds for Elliptic Sombor and Euler-Sombor Indices

Key Points

This survey aims to compile existing extremal results and bounds related to elliptic Sombor and Euler-Sombor indices.
Comprehensive overview of published results related to the elliptic Sombor and Euler-Sombor indices.
Collection of known extremal results and bounds for both indices.
Identification of several open problems in the field.
Summary of established extremal results for the elliptic Sombor index and the Euler-Sombor index.
Presentation of previously unknown bounds that enhance understanding of these indices.
Introduction of open questions that may guide future research.

Abstract

Degree-based topological indices play a central role in chemical graph theory due to their good correlations with physicochemical properties of molecular structures.Among the recently introduced indices, the Sombor index and its variants have attracted significant attention, particularly from the extremal graph theory perspective.Motivated by the geometric interpretation of degree-based indices, the elliptic Sombor index (ESO index, for short) and the Euler-Sombor index (EUSO index, for short) have emerged as novel extensions that enrich the family of Sombor-type indices.In this survey paper, we provide a comprehensive overview of existing results concerning the ESO index and the EUSO index.Particularly, we collect known extremal results and bounds for ESO and EUSO indices.The paper also outlines several open problems.

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