Totally vertex-magic cordial labeling

Abstract

In this paper, we introduce a new labeling called Totally VertexMagic Cordial(TVMC) labeling. A graph G(p, q) is said to be TVMC with a constant C if there is a mapping f : V (G) ∪ E(G) → {0, 1} such that f(a) + ∑ b∈N(a) f(ab)  ≡ C (mod 2) for all vertices a ∈ V (G) and |nf (0)− nf (1)| ≤ 1, where N(a) is the set of vertices adjacent to the vertex a and nf (i)(i = 0, 1) is the sum of the number of vertices and edges with label i. AMS 2010 Mathematics Subject Classification. 05C78.