On the eccentric distance sum of unicyclic graphs with a given matching number

2013/04/16 by Shuchao Li, Yibing Song, Li, Shuchao +3
Computer Science · Mathematics · #05C50 #15A18 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Limits and Structures in Graph Theory #math.CO #msc:05C50 #msc:15A18

paper · pdf · doi:10.48550/arxiv.1304.4335

14 pages, 1 figure

arxiv created 2013/04/16 · openalex publication_date 2013/04/16 · arxiv updated 2013/04/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let G = (V_G,E_G) be a simple connected graph. The eccentric distance sum of G is defined as ξ^d(G)=∑_{v ∈ VG} ε_G(v)D_G(v), where ε_G(v) is the eccentricity of the vertex v and D_G(v)=∑_{u ∈ VG} d(u,v) is the sum of all distances from the vertex v. In this paper, we characterize n-vertex unicyclic graphs with given matching number having the minimal and second minimal eccentric distance sums, respectively.

Citations

• Selected properties of the Schultz molecular topological index

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