Abstract
In this paper, we investigated the edge even graceful labeling property of the join of
two graphs. A function f is called an edge even graceful labeling of a graph
G = (V(G), E(G)) with p = |V(G)| vertices and q = |E(G)| edges if f : E(G) →
{2, 4, ..., 2q} is bijective and the induced function f ∗ : V(G) → {0, 2, 4, ··· , 2q − 2 },
defined as f ∗(x) = ( xy∈E(G) f(xy) ) mod (2k), where k = max(p, q), is an injective
function. Sufficient conditions for the complete bipartite graph Km,n = mK1 + nK1 to
have an edge even graceful labeling are established. Also, we introduced an edge even
graceful labeling of the join of the graph K1 with the star graph K1,n , the wheel graph
Wn and the sunflower graph sfn for all n ∈ N. Finally, we proved that the join of the
graph K2 with the star graph K1,n , the wheel graph Wn and the cyclic graph Cn are
edge even graceful graphs.