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) = \( {array}{c} ∑\ε E(G) {array}\) 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.