Some Characterizations and NP-Complete Problems for Power Cordial Graphs

A power cordial labeling of a graph G = (V(G), E(G)) is a bijection f: V(G) ? {1, 2, ... , |V(G)| } such that an edge e = uv is assigned the label 1 if f(u) = (f(v))(n) or f(v) = (f(u))(n), for some n ? N? {0} and the label 0 otherwise, and satisfy the number of edges labeled with 0 and the number of edges labeled with 1 difer by at most 1. The graph that admits power cordial labeling is called a power cordial graph. In this paper, we derive some characterizations of power cordial graphs as well as explore NP-complete problems for power cordial labeling. This work also rules out any possibility of forbidden subgraph characterization for power cordial labeling.