Recent Advancements in Graph Theory

16Distance Magic and Distance Antimagic Labeling of Some Product Graphs

N P Shrimali

Department of Mathematics,Gujarat University,Ahmedabad,Gujarat (INDIA)E-mail: [e-mail]

Y M Parmar

Department of Mathematics,Gujarat University,Ahmedabad, Gujarat (INDIA)E-mail: [e-mail]

Let G = (V, E) be a graph of order n. Let f:V(G) → {1, 2, …, n} be a bijection. For any vertex q ∈ V(G), the sum ∑p∈N(q)f(p) is called the weight of the vertex q and is denoted by w(q). If there exists a positive integer γ such that w(q) = γ, for every q ∈ V(G), then f is called a distance magic labeling. The constant γ is called the magic constant for f. A graph which admits a distance magic labeling is called a distance magic graph. If w(q) ≠ w(r) for ...