Additive mappings of unweighted directed graphs preserving individual values of the cycle length

Abstract

On the set of unweighted directed graphs on $n$ vertices, the union of graphs is defined as the union of their arc sets. A mapping of graphs is said to be additive if it preserves the union operation. In this paper, a characterization of additive mappings of unweighted directed graphs preserving a fixed value $k\ge 3$ of the cycle length is obtained.