The matching energy of graphs with given edge connectivity

2014/05/07 by Shengjin Ji, Ji, Shengjin, Hongping Ma +1
Computer Science · Materials Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Graphene research and applications

paper · pdf · doi:10.48550/arxiv.1405.1601

openalex publication_date 2014/05/07 · 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 the roots of its matching polynomial. The matching energy of G is defined as the sum ∑_i=1ⁿ|μ_i|. Let K_n-1,1^k be the graph obtained from K₁∪ K_n-1 by adding k edges between V(K₁) and V(K_n-1). In this paper, we show that K_n-1,1^k has maximum matching energy among all connected graph with order n and edge connectivity k.

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