Some Characterizations and NP-Complete Problems for Power Cordial Graphs

Abstract

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 = u v 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 differ 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.