Proximity and remoteness in graphs: A survey

Mustapha Aouchiche; Bilal Ahmad Rather

doi:10.1016/j.dam.2024.04.012

Proximity and remoteness in graphs: A survey

Mustapha Aouchiche
, Bilal Ahmad Rather

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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 done to date.

Original language	English
Pages (from-to)	94-120
Number of pages	27
Journal	Discrete Applied Mathematics
Volume	353
DOIs	https://doi.org/10.1016/j.dam.2024.04.012
Publication status	Published - Aug 15 2024

Keywords

Distance
Extremal graphs
Proximity
Remoteness
Transmission

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2024.04.012

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title = "Proximity and remoteness in graphs: A survey",

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 done to date.",

keywords = "Distance, Extremal graphs, Proximity, Remoteness, Transmission",

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AU - Rather, Bilal Ahmad

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N2 - 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 done to date.

AB - 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 done to date.

KW - Distance

KW - Extremal graphs

KW - Proximity

KW - Remoteness

KW - Transmission

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UR - https://www.scopus.com/pages/publications/85191288883#tab=citedBy

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M3 - Article

AN - SCOPUS:85191288883

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VL - 353

SP - 94

EP - 120

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Proximity and remoteness in graphs: A survey

Abstract

Keywords

ASJC Scopus subject areas

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