PD-prime cordial labeling of graphs

vspace{0.2cm} Let G be a graph and f:V(G)→{1,2,3,.....|V(G)|} be a bijection. Let puv=f(u)f(v) and duv=⎧⎩⎨⎪⎪⎪⎪⎪⎪[f(u)f(v)] if f(u)≥f(v)[f(v)f(u)] if f(v)≥f(u) for all edge uv∈E(G). For each edge uv assign the label 1 if gcd(puv,duv)=1 or 0 otherwise. f is called PD-prime cordial labeling if |ef(0)−ef(1)|≤1 where ef(0) and ef(1) respectively denote the number of edges labelled with 0 and 1. A graph with admit a PD-prime cordial labeling is called PD-prime cordial graph. & & vspace{0.2cm}