3-Difference cordial labeling of some path related graphs

Abstract

Let G be a (p, q)-graph. Let f : V(G) → {1, 2, …, k} be a map where k is an integer, 2 ≤ k ≤ p. For each edge uv, assign the label ∣f(u) − f(v)∣. f is called k-difference cordial labeling of G if ∣v_f(i) − v_f(j)∣ ≤ 1 and ∣e_f(0) − e_f(1)∣ ≤ 1 where v_f(x) denotes the number of vertices labelled with x, e_f(1) and e_f(0) respectively denote the number of edges labelled with 1 and not labelled with 1. A graph with a k-difference cordial labeling is called a k-difference cordial graph. In this paper we investigate 3-difference cordial labeling behavior of triangular snake, alternate triangular snake, alternate quadrilateral snake, irregular triangular snake, irregular quadrilateral snake, double triangular snake, double quadrilateral snake, double alternate triangular snake, and double alternate quadrilateral snake.