A class of totally antimagic total graphs

A total labeling of a graph G is a bijection from the vertex set and edge set of G onto the set {1, 2, ... ,vertical bar V(G)vertical bar + vertical bar E(G)vertical bar}. Such a labeling is vertex-antimagic (edge-antimagic) if all vertex-weights wt(xi)(v) = xi(v) + Sigma vu is an element of E(G) xi(uv), v is an element of V(G), (all edge-weights wt(xi)(vu) = xi(v) + xi(vu) + xi(u), vu is an element of E(G) are pairwise distinct. If a labeling is simultaneously vertex-antimagic and edge-antimagic it is called a totally antimagic total labeling. A graph that admits a totally antimagic total labeling is called a totally antimagic total graph. In this paper we will introduce a large class of totally antimagic total graphs.