Abstract:

Let \( G \) be a graph. An Edouard Product Cordial Labeling (EPCL) of a graph \( G \) with \( |V(G)| = n \) is an injective function \( f : V(G) \rightarrow \{E_0, E_1, E_2, \ldots, E_{n-1}\} \) where \( E_i \) is the \( i \)th Edouard number \( (i = 0,1,2,3,\ldots,n) \) that induces a function \( f^* \) defined by

\(
f^*(uv) = (f(u)f(v)) \; (\text{mod } 2)
\)

for all edge \( e = uv \) such that \( |e_f^*(0) – e_f^*(1)| \leq 1 \) where \( e_f^*(0) \) is the number of vertices labeled with 0 and \( e_f^*(1) \) is the number of vertices labeled with 1. The graph that satisfies the condition of an edouard product cordial labeling is called an edouard product cordial graph (EPCG).