  Let $G=C_{p^n}$ be a finite cyclic p-group, and let $Hol(G)$ denote its
holomorph. In this work, we find and characterize the regular subgroups of
$Hol(G)$ that are mutually normalizing each other in the permutation group
$Sym(G)$. We represent such regular subgroups as vertices of a graph, and we
connect a pair of them by an edge when they mutually normalize each other. The
approach to construct this local normalizing graph relies on the theory of
gamma functions, and the final result will contain all the information about
the regular subgroups of $Hol(G)$ in a compact form.
