Further results on super graceful labeling of graphs
Gee-Choon Lau, Wai Chee Shiu, Ho-Kuen Ng · AKCE International Journal of Graphs and Combinatorics · 2016
Let be a simple, finite and undirected graph of order and size . A bijection such that for every edge is said to be a -super graceful labeling of . We say is -super graceful if it admits a -super graceful labeling. For , the function is 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 graphs , 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.