D. Jayantara, Purwanto, S. Irawati
Elsonbaty and Daoud introduced a labeling of graph with p vertices and q edges called edge even graceful labeling i.e. a bijective function f of the edge set E(G) into the set {2,4,6, ⋯, 2q} such that the induced function f∗:V(G) → {0,2,4, ⋯, 2k - 2}, defined as f∗(x) = (∑ xy∈E(G) f(xy)) mod(2k), is an injective function, where k = max(p, q). The corona G 1 G 2 of graphs G 1 and G 2 is the graph obtained by taking one copy of G 1, which has p 1 vertices, and p 1 copies of G 2, and then joining the ith vertex of G 1 by an edge to every vertex in the ith copy of G2 . Some path and cycle-related graph which are edge even graceful has been studied by Elsonbaty and Daoud. This study we construct the corona graph of P 2 and Pn and the corona of Sn and K 1. In this paper, we prove that P 2 Pn, when n ≡ 0,4, or 6 mod(8), and (Sn K 1) - v 0, when n is even and v 0 is a vertex of degree 1 joining to the center of the star Sn, are admit edge even graceful labeling. © Published under licence by IOP Publishing Ltd.
Department of Mathematics, Universitas Negeri Malang, Jalan Semarang 5, Malang, 65145, Indonesia
