STRUCTURAL ANALYSIS OF THE STATUS ELLIPTIC SOMBOR INDEX AND ITS CHEMICAL APPLICATIONS TO OCTANE ISOMERS
Vijendra N., Jalappa, Boregowda H. S.
Department of Studies and Research in Mathematics, Tumkur University, Tumkur-572103, Karnataka, India
Abstract : In a graph G, the status σ(α) of a vertex α is given by σ(α) = ∑ (β ∈ V(G)) d(α, β), where V(G) represents the vertex set and d(α, β) denotes the distance between α and β in G. The status elliptic Sombor index (SESO) is defined as SESO(G) = ∑ (αβ ∈ E(G)) (σ(α) + σ(β)) √(σ(α)² + σ(β)²), where E(G) is the edge set of the graph G. In this paper, we investigate the comparative analysis of molecular graphs of octane isomers with status-based indices, observing that the status elliptic Sombor index attains the highest value among them. Additionally, we establish certain bounds for this index in terms of diameter and other status-based indices. Furthermore, we compute exact values of the status elliptic Sombor index for specific graph classes.
Mathematics Subject Classification (2020): 05C07, 05C12.
Keywords : Distance, status of a vertex, elliptic Sombor index, status elliptic Sombor index.
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