Edge Induced V\ (₄\) −Magic Labeling of Line Graphs

Let V4 = 0, a, b, c be the Klein-4-group with the elements a, b, c have order 2 and 0 be the identity element. Let G = (V (G), E (G) ) be a simple, connected, finite and undirected 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 \ 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 (Libeeshkumar and Kumar, 2020a), 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 discusses some results related to the EIML of line graphs and provides a characterization of the EIML of line graphs for certain well-known named graphs.