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 Z₃ product magic labeling. A digraph G(p, q) is said to admit Z₃-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.