Edge Induced V4−Magic Labeling of Subdivision Graphs

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) = \(\begin{array}{c}\sum\\{uv \in E(G)}\end{array}\)f(uv) for all u \(\in\) 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.