Ordering of bicyclic graphs by matching energy

2017/04/07 by Xiangxiang Liu, Liu, Xiangxiang, Ligong Wang +3 · 1 citation
Chemistry · Mathematics · #05C35 #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.1704.02068

openalex publication_date 2017/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a simple graph of order n and μ₁,μ₂,…,μ_n be the roots of its matching polynomial. The matching energy is defined as the sum ∑ⁿ_i=1|μ_i|, which was introduced by Gutman and Wagner in 2012. In this paper, the graphs with the first five smallest matching energies among all bicyclic graphs for order n>5 are determined.

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