The strong-connectivity of word-representable digraphs
Combinatorics
2011-08-31 v2
Abstract
A word-graph Gw is a digraph represented by a word w such that the vertex-set V(Gw) is the alphabet of w and the edge-set E(Gw) is determined by non-identical adjacent letter pairs in w. In this paper we study the strong-connectivity of word-graphs. Our main result is that the number of strongly connected word-graphs represented by l-words of over an n-alphabet can be expressed via a recurrence relation T(l,n) on the Stirling numbers of the second kind using a link between word partitions and digraph connectivity.
Cite
@article{arxiv.1102.0980,
title = {The strong-connectivity of word-representable digraphs},
author = {Edward J. L. Bell and Damon Berridge and Paul Rayson},
journal= {arXiv preprint arXiv:1102.0980},
year = {2011}
}
Comments
12 pages, 4 figures