Abstract
For any positive integer m, we assign a digraph G(m) for
which {0, 1, 2, 3, ..., m−1} is the set of vertices and there is an edge from
a vertex u to a vertex v if m divides u
7 − v. We enumerate the self and
isolated loops and study the structures of this digraph for the numbers 2
r
and 7
r
, for every positive integer r. Further, we characterize the existence
of cycles by employing Carmichael’s Theorem. Also, we discuss the subdigraphs of proposed digraph induced by the vertices coprime to m and
not coprime to m. Lastly, we characterize the regularity, semiregularity
and results regarding components of these subdigraphs.
