On cordial, magicness and cordial deficiency of paley digraphs

In this paper we prove that a small class of digraph called Paley digraph with q vertices and pq edges where q is a prime number congruent to 3 (mod4) and p = q -1 / 2 admits Z
₃
product magic labeling. A digraph G(p, q) is said to admit Z
₃
-product magic labeling if there exists a function f from E onto the set {1, 2} such that the induced map f* on V defined by f*(v
_i
) ={Πf(v
_j
v
_i
) | v
_j
v
_i
∈ E} (mod 3) = k, a constant. The minimum number of edges, taken over all friendly labeling of G, which it is necessary to add in order that the resulting graph G' become cordial is called cordial edge deficiency of G. We extend the above deficiency for a directed graph called Paley digraph. Also we calculate the signed product cordial edge deficiency, total edge cordial deficiency and total sequential cordial deficiency of the same graph.