Totally magic cordial labeling of some graphs

Document Type: Research Paper


1 2Research Center, Department of Mathematics, Aditanar College for women, Tiruchendur - 628 216, India

2 Department of Mathematics, Sri enakshi Government Arts College for Women (Autonomous), Madurai - 625 002, India.


A graph G is said to have a totally magic cordial labeling with constant C if there exists a mapping f : V (G) ∪ E(G) → {0, 1} such that f(a) + f(b) + f(ab) ≡ C (mod 2) for all ab ∈ E(G) and |nf (0) − nf (1)| ≤ 1, where nf (i) (i = 0, 1) is the sum of the number of vertices and edges with label i. In this paper, we give a necessary condition for an odd graph to be not totally magic cordial and also prove that some families of graphs admit totally magic cordial labeling.