COMPLEMENTARY TOTALLY ANTIMAGIC TOTAL GRAPHS

For a graph G, with the vertex set V(G) and the edge set E(G), a total labeling is a bijection f from V (G) U E(G) to the set of integers {1, 2, …, |V (G) |+| E(G) |}. The edge weight sum is f(u)+f(uv)+f(v) = k  for every edge uv є E(G) and the vertex weight sum is f(u)+∑ᵥЄV (G ) f(uv) = k1 for vertex vєV(G) where k and k1 are constants called valences. If k’s(k1’s) are different, a total labeling is called edge antimagic. total (vertex antimagic total). If a labeling is simultaneously edge-antimagic total and vertex antimagic total it is called a totally antimagic total labeling. A graph that admits totally antimagic total labeling is said to be totally antimagic total graph. Given totally antimagic total labeling f of G then, the function f(x)  is such that  f(x)= |V (G) + |E(G)| + 1 - f(x) for all  X є V (G) U E(G) is said to be complementary to f(x) or Complementary totally antimagic total labeling (CTAT). In this paper we establish complementary totally antimagic total labeling of some family of graphs Join G + K1, Paths Pn, Cycles Cn, Stars S1;n, Double Stars Bm;n, Wheels Wn and Corana GonK1: