## $n$-Functional digraphs uniquely determined by the skeleton

### Volume 91 / 2002

Colloquium Mathematicum 91 (2002), 79-89
MSC: 04A05, 05C20, 05C78, 05C99.
DOI: 10.4064/cm91-1-6

#### Abstract

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.