Further results on edge even graceful labeling of the join of two graphs | ||||
| Journal of the Egyptian Mathematical Society | ||||
| Volume 28, Issue 1, June 2020, Page 1-20 PDF (1.59 MB) | ||||
| DOI: 10.1186/s42787-020-00077-5 | ||||
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| Authors | ||||
| Mohamed R. Zeen El Deen; Nora A. Omar | ||||
| Department of Mathematics, Faculty of Science, Suez University, Suez, Egypt | ||||
| Abstract | ||||
| 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. | ||||
| Keywords | ||||
| Complete bipartite graph; Wheel graph; Sunflower graph; Edge even graceful labeling; Join of two graphs | ||||
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