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September 10, 2025Open Access

Edge Induced V4−Magic Labeling of Subdivision Graphs

Key Points

The study reveals that an edge induced V4-magic graph has a constant function for the edge labeling.
Key findings include the established relationship between edge labeling and vertex labeling in graph structures.
The approach utilizes mathematical constructs like f and f++ to define and characterize edge induced V4-magic labeling.
These results may enable further exploration into graph theory applications and more complex labeling scenarios.

Abstract

Let V4 = 0, a, b, c be the Klein-4-group with identity element 0 and G = (V (G), E (G) ) be a graph. Let f: E (G) → V4∖0 be an edge labeling and f+: V (G) → V4 denotes the induced vertex labeling of f defined by f+ (u) = \ (arrayc\\uv E (G) array\) f (uv) for all u \ (\) V (G). Then f+ again induces an edge labeling f++: E (G) → V4 defined by f++ (uv) = f+ (u) + f+ (v), for all uv ∈ E (G). A graph G = (V (G), E (G) ) is said to be an edge induced V4-magic graph, if there exists an edge labeling f for which the function f++ is a constant function. The function f, so obtained is called an Edge Induced V4-Magic Labeling (EIML) of G. The present paper deals with basic results regarding EIML of subdivision graphs and the characterization of EIML of subdivision of certain named graphs.

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