2018/07/03 by Lau, Gee-Choon, Shiu, Wai-Chee, Ng, Ho-Kuen
#05C78 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1807.01203
Let G=(V(G),E(G)) be a simple, finite and undirected graph of order p and size q. For k≥ 1, a bijection f: V(G)∪ E(G) → \k, k+1, k+2, …, k+p+q-1\ such that f(uv)= |f(u) - f(v)| for every edge uv∈ E(G) is said to be a k-super graceful labeling of G. We say G is k-super graceful if it admits a k-super graceful labeling. In this paper, we study the k-super gracefulness of some standard graphs. Some general properties are obtained. Particularly, we found many sufficient conditions on k-super gracefulness for many families of (complete) bipartite and tripartite graphs. We show that some of the conditions are also necessary.