Further results on 3−remainder cordial labeling of graphs

Let G be a (p, q) graph. Let f be a function from V (G) to the set (1, 2, …, k) where k is an integer 2 < k ≤ |V (G)|. For each edge uv assign the label r where r is the remainder when f(u) is divided by f(v) (or) f(v) is divided by f(u) according as f(u) ≥ f(v) or f(v) ≥ f(u). Then the function f is called a k-remainder cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ (1, …, k) where vf (x) denote the number of vertices labelled with x and |ηe (0)-ηo (1)| ≤ 1 where ηe (0) and ηo (1) respectively denote the number of edges labelled with an even integers and number of edges labelled with an odd integers. A graph admits a k-remainder cordial labeling is called a k-remainder cordial graph. In this paper we investigate the 3-remainder cordial labeling behavior of the subdivision of the star, wheel, subdivision of the wheel, subdivision of the comb, armed crown, fan, square of the path, K_{1, n} O K₂, etc,.