Total Bimagic labeling and Total Magic Cordial labeling of Paley digraphs

Abstract

In this paper we define Total Bimagic labeling and Total Magic Cordial labeling fordigraphs, and we prove the same for the small class of digraphs called Paley digraphs with q vertices and p set of edges where q 3 mod 4 and p = (q-1/2) admits and Total Magic Cordiallabeling Total Bimagic labeling. A digraph G is said to have a total magic cordial (TMC) labeling with constant C if thereexists a mapping f: V (G) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∪</sup> E(G) {0, 1} such that for any vertex vi, the sum of the labels of outgoing edges of vi and the label of itself is a constant C (mod2) provided the condition |f(0)-f(1)|≤ 1 is hold, where f(0) = vf (0)+ef (0) and f(1) = vf(1) + ef(1) where Vf(l), ef(l); i to,{0, 1} are respectively, the number of vertices and edges labeled with i.A total bimagic labeling of a digraph with v vertices and e edges is a bijection f : V(G) E(G) {1,2, .... V E| such that for any vertex vi the sum of the labels of outgoing edges of vi together with the label of itself is equal to either of constants kl or k2. AMS Subject Classification: 05C78.