A metric on the set of connected simple graphs of given order

Kiran R. Bhutani, Bilal Khan

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We introduce a sequence dnl (l = 1, 2, . . .) of functions on fraktur G signn × fraktur G signn, where fraktur G signn is the set of all simple, connected, undirected graphs of order n up to isomorphism. We show that when l = 1 or l ≥ n - 1, dnl is a metric on fraktur G sign n. While (fraktur G signn, dn1) is a totally disconnected metric space that embodies the classical notion of graph isomorphism, (fraktur G signn, dnl) is a connected metric space whenever l ≥ n - 1. In this paper, we investigate some properties and the relationship between these two spaces. This work was motivated by the problem of virtual path layout in high-speed computer networks, which concerns embedding a specified virtual network into the given physical network in a way that makes optimal use of the physical network resources.

Original languageEnglish (US)
Pages (from-to)232-240
Number of pages9
JournalAequationes Mathematicae
Volume66
Issue number3
DOIs
StatePublished - Dec 1 2003

Fingerprint

Computer networks
Simple Graph
Connected graph
Metric
Metric space
Graph Isomorphism
High-speed Networks
Computer Networks
Undirected Graph
Layout
Isomorphism
Path
Resources

Keywords

  • Distance between graphs
  • Graph embeddings
  • Virtual path layout

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

A metric on the set of connected simple graphs of given order. / Bhutani, Kiran R.; Khan, Bilal.

In: Aequationes Mathematicae, Vol. 66, No. 3, 01.12.2003, p. 232-240.

Research output: Contribution to journalArticle

@article{9320379dccd14c80b2c985395f7e719b,
title = "A metric on the set of connected simple graphs of given order",
abstract = "We introduce a sequence dnl (l = 1, 2, . . .) of functions on fraktur G signn × fraktur G signn, where fraktur G signn is the set of all simple, connected, undirected graphs of order n up to isomorphism. We show that when l = 1 or l ≥ n - 1, dnl is a metric on fraktur G sign n. While (fraktur G signn, dn1) is a totally disconnected metric space that embodies the classical notion of graph isomorphism, (fraktur G signn, dnl) is a connected metric space whenever l ≥ n - 1. In this paper, we investigate some properties and the relationship between these two spaces. This work was motivated by the problem of virtual path layout in high-speed computer networks, which concerns embedding a specified virtual network into the given physical network in a way that makes optimal use of the physical network resources.",
keywords = "Distance between graphs, Graph embeddings, Virtual path layout",
author = "Bhutani, {Kiran R.} and Bilal Khan",
year = "2003",
month = "12",
day = "1",
doi = "10.1007/s00010-003-2687-5",
language = "English (US)",
volume = "66",
pages = "232--240",
journal = "Aequationes Mathematicae",
issn = "0001-9054",
publisher = "Birkhauser Verlag Basel",
number = "3",

}

TY - JOUR

T1 - A metric on the set of connected simple graphs of given order

AU - Bhutani, Kiran R.

AU - Khan, Bilal

PY - 2003/12/1

Y1 - 2003/12/1

N2 - We introduce a sequence dnl (l = 1, 2, . . .) of functions on fraktur G signn × fraktur G signn, where fraktur G signn is the set of all simple, connected, undirected graphs of order n up to isomorphism. We show that when l = 1 or l ≥ n - 1, dnl is a metric on fraktur G sign n. While (fraktur G signn, dn1) is a totally disconnected metric space that embodies the classical notion of graph isomorphism, (fraktur G signn, dnl) is a connected metric space whenever l ≥ n - 1. In this paper, we investigate some properties and the relationship between these two spaces. This work was motivated by the problem of virtual path layout in high-speed computer networks, which concerns embedding a specified virtual network into the given physical network in a way that makes optimal use of the physical network resources.

AB - We introduce a sequence dnl (l = 1, 2, . . .) of functions on fraktur G signn × fraktur G signn, where fraktur G signn is the set of all simple, connected, undirected graphs of order n up to isomorphism. We show that when l = 1 or l ≥ n - 1, dnl is a metric on fraktur G sign n. While (fraktur G signn, dn1) is a totally disconnected metric space that embodies the classical notion of graph isomorphism, (fraktur G signn, dnl) is a connected metric space whenever l ≥ n - 1. In this paper, we investigate some properties and the relationship between these two spaces. This work was motivated by the problem of virtual path layout in high-speed computer networks, which concerns embedding a specified virtual network into the given physical network in a way that makes optimal use of the physical network resources.

KW - Distance between graphs

KW - Graph embeddings

KW - Virtual path layout

UR - http://www.scopus.com/inward/record.url?scp=0345759878&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0345759878&partnerID=8YFLogxK

U2 - 10.1007/s00010-003-2687-5

DO - 10.1007/s00010-003-2687-5

M3 - Article

VL - 66

SP - 232

EP - 240

JO - Aequationes Mathematicae

JF - Aequationes Mathematicae

SN - 0001-9054

IS - 3

ER -