On the relationship between the diameter and the size of a boundary of a directed graph

Shuji Jinbo, Akira Marouka

Research output: Contribution to journalArticle

Abstract

A family of expanding graphs is useful to make many kind of networks efficient, as Ajtai et al. constructed sorting networks of depth O(log n) with it. On the other hand, Klawe showed that particular families of directed graphs obtained from a finite number of one-dimensional linear functions, which play important roles in constructing some kind of networks or generating random numbers, cannot be families of expanding graphs. Moreover, Klawe gave a conjecture concerning a lower bound of the amount of expanding property of these families. Maass gave a partial answer to the conjecture. In this paper, a theorem that states the relationship between the diameter and the size of a boundary in a directed graph is proved. An answer to Klawe's conjecture is also obtained from this theorem. The answer is more suitable than Maass's one.

Original languageEnglish
Pages (from-to)277-282
Number of pages6
JournalInformation Processing Letters
Volume50
Issue number5
DOIs
Publication statusPublished - Jun 10 1994
Externally publishedYes

Fingerprint

Directed graphs
Directed Graph
Sorting
Sorting Networks
Random number
Graph in graph theory
Theorem
Linear Function
Lower bound
Partial
Relationships
Family

Keywords

  • Boundaries
  • Combinatorial problems
  • Diameter
  • Expanding graphs
  • Linear functions

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

On the relationship between the diameter and the size of a boundary of a directed graph. / Jinbo, Shuji; Marouka, Akira.

In: Information Processing Letters, Vol. 50, No. 5, 10.06.1994, p. 277-282.

Research output: Contribution to journalArticle

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