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The Exponents of Strongly Connected Graphs

Published online by Cambridge University Press:  20 November 2018

Edward A. Bender  and
Thomas W. Tucker
Edward A. Bender
Affiliation:
Institute for Defense Analyses, Princeton, New Jersey
Thomas W. Tucker
Affiliation:
Dartmouth College, Hanover, New Hampshire
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A directed graphG is a set of vertices V and a subset of V × V called the edges of G. A path in G of length k,

is such that (vi, vi+1) is an edge of G for 1 ≦ i ≦ k. A directed graph G is strongly connected if there is a path from every vertex of G to every other vertex. A circuit is a path whose two end vertices are equal. An elementary circuit has no other equal vertices. See (1) for a fuller discussion.

Let G be a finite, strongly connected, directed graph (fscdg). The kth power Gk of G is the directed graph with the same vertices as G and edges of the form (i, j) where G has a path of length k from i to j.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 769 - 782
Copyright
Copyright © Canadian Mathematical Society 1969

References

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