3-Divisor Cordial Labeling of some Join Graphs

Abstract

Let G be a (p, q) graph and 2 ≤ k ≤ p. Let f : V (G) → {1, 2, ... , k} be a map. For each edge uv, assign the label 1 if either f(u) or f(v) divides the other and 0 otherwise. f is called a k-divisor cordial labeling if |v_f (i) - v_f (j)| ≤ 1, i, j ∈ {1, 2, ... , k} and |e_f (0) - e_f (1)| ≤ 1 where v_f (x) denotes the number of vertices labeled with x, where x ∈ {1, 2, ... , k}, e_f (i) denote the number of edges labeled with i, i ∈ {0, 1}. A graph with a k-divisor cordial labeling is called a k-divisor cordial graph. In this paper, we discuss 3-divisor cordial labeling behavior of wheel and K_n + 2K₂.

Key words and phrases. cycle, join, wheel, complete graph.

2000 Mathematics Subject Classification. 05C78