The multiplicative Zagreb indices of graphs with given connectivity or number of pendant vertices

2017/11/24 by Shengjin Ji, Shaohui Wang, Ji, Shengjin +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.1711.09014

openalex publication_date 2017/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a graph G, the first multiplicative Zagreb index ∏₁(G) is the product of squares of vertex degrees, and the second multiplicative Zagreb index ∏₂(G) is the product of products of degrees of pairs of adjacent vertices. In this paper, we explore graphs with extremal Π₁(G) and Π₂(G) in terms of (edge) connectivity and pendant vertices. The corresponding extremal graphs are characterized with given connectivity at most k and p pendant vertices. In addition, the maximum and minimum values of ∏₁(G) and ∏₂(G) are provided. Our results extend and enrich some known conclusions.

Citations

• Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons

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