4-Total difference cordial graphs obtained from path and cycle

Abstract

 Let G be a graph. Let f : V (G) → {0, 1, 2, . . . , k − 1} be a map where k ∈ N and k > 1. For each edge uv, assign the label |f(u) − f(v)|.  f  is called k-total difference cordial labeling  of  G  if  |t_df(i) – t_df (j)|  ≤  1,  i, j  ∈  {0, 1, 2, . . . , k − 1} where t_df(x) denotes the total number of vertices and the edges labeled with x. A graph with admits a k-total difference cordial labeling  is called k-total difference cordial graphs. In this paper we investigate the 4-total difference cordial labeling behaviour of   , ().