The Exponents of Strongly Connected Graphs
Edward A. Bender, Thomas W. Tucker · Canadian Journal of Mathematics · 1969
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.