Existence and non existence of mean cordial labeling of certain graphs

Abstract

Let f be a function from the vertex set V(G)V(G) to 0,1,20,1,2. For each edge uvuv assign the label f(u)+f(v)2f(u)+f(v)2. ff is called a mean cordial labeling if |vf(i)−vf(j)|≤1|vf(i)−vf(j)|≤1 and |ef(i)−ef(j)|≤1|ef(i)−ef(j)|≤1, i,j∈0,1,2i,j∈0,1,2, where vf(x)vf(x) and ef(x)ef(x) respectively denote the number of vertices and edges labeled with xx (x=0,1,2)(x=0,1,2). A graph with a mean cordial labeling is called a mean cordial graph. In this paper we investigate mean cordial labeling behavior of prism, K2+¯¯¯¯¯¯¯¯KmK2+Km¯, Kn+¯¯¯¯¯¯¯¯¯¯2K2Kn+2K2¯, book BmBm and some snake graphs.