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.
Muhammad Haris Mateen, Muhammad Khalid Mahmood. (2019) Power Digraphs Associated with the Congruence x n ≡ y (mod m), Punjab University Journal of Mathematics, Volume 51, Issue 5.
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