Some 3-Divisor Cordial Graphs Derived from Path

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 xy, assign the label 1 if either f(x) or f(y) 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 obtain 3-divisor cordial graphs derived from path.

Key words and phrases. path, union, connected graph, divisor cordial.

2000 Mathematics Subject Classification. 05C78