We show that any total n-functional digraph D is uniquely determined by its skeleton up to the orientation of some cycles and infinite chains. Next, we characterize all graphs G such that each n-functional digraph obtained from G by directing all its edges is total. Finally, we describe finite graphs whose edges can be directed to form a total n-functional digraph without cycles.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-1-6,
author = {Konrad Pi\'oro},
title = {n-Functional digraphs uniquely determined by the skeleton},
journal = {Colloquium Mathematicae},
volume = {91},
year = {2002},
pages = {79-89},
zbl = {0986.05053},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-1-6}
}
Konrad Pióro. n-Functional digraphs uniquely determined by the skeleton. Colloquium Mathematicae, Tome 91 (2002) pp. 79-89. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-1-6/