Bounds on Trees with Topological Indices Among Degree Sequence

2025/05/18 by Hamoud, Jasem, Belov-Kanel, Alexei, Abdullah, Duaa
#05C05 #05C12 #05C35 #68R10 #Combinatorics (math.CO) #FOS: Mathematics #G.2.2

paper · doi:10.48550/arxiv.2505.12518

Abstract

In this paper, we investigate The relationship between the Albertson index and the first Zagreb index for trees. For a tree T=(V,E) with n=|V| vertices and m=|E| edges, we provide several bounds and exact formulas for these two topological indices, and we show that the Albertson index \irr(T) and the first Zagreb index M₁(T) satisfy the association irr(T)=d₁²+d_n²+(n-2)((Δ+ δ)/(2))²+∑_i=2^n-1 d_i+d_n - d₁-2n-2. Our goal of this paper is provide a topological indices, Albertson index, Sigma index among a degree sequence \mathscrD=(d₁,…,d_n) where it is non-increasing and non-decreasing of tree T.

Related

• Topological Indices With Degree Sequence \mathscrD of Tree
• On Topological Indices in Trees: Fibonacci Degree Sequences and Bounds
• Degree Sequence of Albertson and σ-Indices on Trees of Order n\geqslant 3
• Bounds on the Albertson Index for Trees with Given Degree Sequences
• Topological Indices Among Strong Support Vertex