22、(2, 3)-Cordial Oriented Hypercubes: An In - Depth Exploration

(2, 3)-Cordial Oriented Hypercubes: An In - Depth Exploration

1. Basic Concepts

1.1 Digraph Sets

• Set (D_n) : It is the set of all digraphs with (n) vertices.
• Set (T_n) : A subset of (D_n) that consists of all digon - free digraphs. A digon is a 2 - cycle in a digraph.

1.2 Labeling Definitions

• Vertex Labeling : Given a digraph (D=(V, A)), a vertex labeling (f:V\rightarrow{0, 1}) assigns either 0 or 1 to each vertex.
• Arc Labeling : An induced arc labeling (g:A\rightarrow{0, 1, - 1}) is defined as (g(\overrightarrow{uv})=f(v)-f(u)) for an arc (\overrightarrow{uv}) in (A).
• Function (\Lambda_{f,