Further Results on 3-Difference Cordial Graphs

Let \( G \) be a \( (p, q) \) graph. Let \( f : V(G) \to \{1, 2, \ldots, k\} \) be a map where \( k \) is an integer \( 2 \leq k \leq p \). For each edge \( uv \), assign the label \( |f(u) – f(v)| \). \( f \) is called \( k \)-difference cordial labeling of \( G \) if \( |v_f(i) – v_f(j)| \leq 1 \) and \( |e_f(0) – e_f(1)| \leq 1 \), where \( v_f(x) \) denotes the number of vertices labeled with \( x \), \( e_f(1) \) and \( e_f(0) \) respectively denote the number of edges labeled with 1 and not labeled 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 slanting ladder, book with triangular pages, middle graph of a path, shadow graph of a path, triangular ladder, and the armed crown.