16Distance Magic and Distance Antimagic Labeling of Some Product Graphs

N P Shrimali

Department of Mathematics,Gujarat University,Ahmedabad,Gujarat (INDIA)E-mail: narenp05@gmail.com

Y M Parmar

Department of Mathematics,Gujarat University,Ahmedabad, Gujarat (INDIA)E-mail: ymp.maths@gmail.com

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 $\sum _{p\in N(q)}f(p)$ 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 ...

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