Comparison of Wiener index and Zagreb eccentricity indices

2019/12/13 by Kexiang Xu, Xu, Kexiang, Kinkar Chandra Das +5
Chemistry · Computer Science · Mathematics · #Combinatorics (math.CO) #Computational Drug Discovery Methods #FOS: Mathematics #Graph theory and applications #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.1912.06335

openalex publication_date 2019/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The first and the second Zagreb eccentricity index of a graph G are defined as E₁(G)=∑_{v∈ V(G)}ε_G(v)² and E₂(G)=∑_{uv∈ E(G)}ε_G(u)ε_G(v), respectively, where ε_G(v) is the eccentricity of a vertex v. In this paper the invariants E₁, E₂, and the Wiener index are compared on graphs with diameter 2, on trees, on a newly introduced class of universally diametrical graphs, and on Cartesian product graphs. In particular, if the diameter of a tree T is not too big, then W(T) ≥ E₂(T) holds, and if the diameter of T is large, then W(T) < E₁(T) holds.

Citations

• Eccentric Connectivity Index: A Novel Highly Discriminating Topological Descriptor for Structure−Property and Structure−Activity Studies

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