Proximity and Remoteness in Graphs: a survey

2023/10/01 by Mustapha Aouchiche, Aouchiche, Mustapha, Bilal Ahmad Rather +1 · 2 citations
Computer Science · #05C12 #05C35 #15A18 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Interconnection Networks and Systems

paper · pdf · doi:10.48550/arxiv.2310.12777

openalex publication_date 2023/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The proximity π= π(G) of a connected graph G is the minimum, over all vertices, of the average distance from a vertex to all others. Similarly, the maximum is called the remoteness and denoted by ρ= ρ(G). The concepts of proximity and remoteness, first defined in 2006, attracted the attention of several researchers in Graph Theory. Their investigation led to a considerable number of publications. In this paper, we present a survey of the research work.

Cited by

• Remoteness, order, size and connectivity constraints in digraphs
• On Proximity and other Distance Parameters in Planar Graphs

Related

• Proximity and remoteness in triangle-free and C₄-free graphs in terms\n of order and minimum degree
• Remoteness of graphs with given size and connectivity constraints
• On Proximity and other Distance Parameters in Planar Graphs
• On the difference between proximity and other distance parameters in triangle-free graphs and C₄-free graphs
• Remoteness and distance eigenvalues of a graph