MODIFIED SOMBOR INDEX OF TREES

MODIFIED SOMBOR INDEX OF TREES

N. Dehgardi

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Abstract

The modified Sombor index of a graph G, denoted by mSO(G), is defined as the sum of weights q 1 d2 G (u)+d2 G (v) of all edges uv of E(G), where dG(u) denotes the degree of a vertex u in G. In this paper we show that for any tree T of order n with maximum degree Δ, mSO(T) ≤ Δ √ Δ2 + 4 + (n − 2Δ − 1) √ 8 + Δ √ 5 , when Δ ≤ n−1 2 and mSO(T) ≤ (2Δ + 1 − n) √ Δ2 + 1 + (n − Δ − 1) √ Δ2 + 4 + (n − Δ − 1) √ 5 , when Δ > n−1 2 . Also we determine the extremal trees achieve these bounds.

Keywords

Sombor index, Modified Sombor index, Upper bound, Tree.