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Resolving an open problem on the modified Sombor index for bicyclic graphs

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  • Chandra Das, Kinkar
  • Bera, Jayanta

Abstract

Topological indices are quantitative measures that characterize the structural attributes of molecules via their graphical representations. In chemical graph theory, these indices have been widely utilized to predict several physico-chemical properties of molecules. Recently, Kulli and Gutman introduced a variant of the Sombor index, known as the modified Sombor index. For a graph G, the modified Sombor index (MSO) is defined asMSO(G)=∑vxvy∈E(G)1dx2+dy2,where dx and dy denote the degrees of the vertices vx and vy, respectively. In a recent study, Huang and Liu [Bounds of modified Sombor index, spectral radius and energy, AIMS Mathematics 6 (2021) 11263–11274] posed an open problem concerning the extremal graphs of the MSO index among all bicyclic graphs of order n. In the present work, we solve this problem by characterizing the bicyclic graphs of order n that minimize the MSO index. Furthermore, we investigate the chemical relevance of the MSO index and provide a comparative analysis with several variants of the Sombor index.

Suggested Citation

  • Chandra Das, Kinkar & Bera, Jayanta, 2026. "Resolving an open problem on the modified Sombor index for bicyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 531(C).
    • Handle: RePEc:eee:apmaco:v:531:y:2026:i:c:s0096300326002328
    DOI: 10.1016/j.amc.2026.130180
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