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.
Zeen El Deen, M., & Omar, N. (2020). Further results on edge even graceful labeling of the join of two graphs. Journal of the Egyptian Mathematical Society, 28(1), 1-20. doi: 10.1186/s42787-020-00077-5
MLA
Mohamed R. Zeen El Deen; Nora A. Omar. "Further results on edge even graceful labeling of the join of two graphs", Journal of the Egyptian Mathematical Society, 28, 1, 2020, 1-20. doi: 10.1186/s42787-020-00077-5
HARVARD
Zeen El Deen, M., Omar, N. (2020). 'Further results on edge even graceful labeling of the join of two graphs', Journal of the Egyptian Mathematical Society, 28(1), pp. 1-20. doi: 10.1186/s42787-020-00077-5
VANCOUVER
Zeen El Deen, M., Omar, N. Further results on edge even graceful labeling of the join of two graphs. Journal of the Egyptian Mathematical Society, 2020; 28(1): 1-20. doi: 10.1186/s42787-020-00077-5
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