期刊名称：AKCE International Journal of Graphs and Combinatorics
印刷版ISSN：0972-8600
出版年度：2016
卷号：13
期号：2
页码：200-209
DOI：10.1016/j.akcej.2016.06.002
语种：English
出版社：Elsevier
摘要：AbstractLetG=(V(G),E(G))be a simple, finite and undirected graph of orderpand sizeq. A bijectionf:V(G)∪E(G)→{k,k+1,k+2,…,k+p+q−1}such thatf(uv)=|f(u)−f(v)|for every edgeuv∈E(G)is said to be ak-super graceful labeling ofG. We sayGisk-super graceful if it admits ak-super graceful labeling. Fork=1, the functionfis called a super graceful labeling and a graph is super graceful if it admits a super graceful labeling. In this paper, we study the super gracefulness of complete graph, the disjoint union of certain star graphs, the complete tripartite graphsK(1,1,n), and certain families of trees. We also present four methods of constructing new super graceful graphs. In particular, all trees of order at most 7 are super graceful. We conjecture that all trees are super graceful.
