




A Classification of Cyclic Nodes and Enumeration of Components of a Class of Discrete Graphs 

PP: 103112 

Author(s) 

M. Khalid Mahmood,
Farooq Ahmad,


Abstract 

Let Zn be the ring of residue classes modulo n. Define f : Zn 7→ Zn by f (x) = x4. Action of this map is studied by means
of digraphs which produce an edge from the residue classes a to b if f (a) ≡ b. For every integer n, an explicit formula is given for the
number of fixed points of f . It is shown that the graph G(pk), k ≥ 1 has four fixed points if and only if 3  p−1 and has two fixed
points if and only if 3 ∤ p−1. A classification of cyclic vertices of the graph G(pk) has been determined. A complete enumeration of
nonisomorphic cycles and components of G(pk) has been explored. 




