The Extremal Sigma Index of Connected Graphs with Given Number of Pendant Vertices

2023 · doi:10.21203/rs.3.rs-2646370/v1
preprint OA: closed
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Abstract

Abstract The Sigma index of a graph G = (V,E) is defined as the sum of (d(u)−d(υ))2 over all edges uυ ∈ E, where d(υ) denotes the degree of the vertex u in G. In this paper, we completely determine the extremal values of the Sigma index of connected graphs with n vertices and p pendant vertices (1 ≤ p ≤ n − 1), and characterize the corresponding extremal graphs.

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last seen: 2026-05-19T01:45:01.086888+00:00