Document Type
Journal Article
Department/Unit
Department of Mathematics
Language
English
Abstract
Let G=(V(G),E(G)) be a simple, finite and undirected graph of order p and size q. 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. For k=1, the function f 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 K(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.
Keywords
Graceful labeling, Super graceful labeling, Tree
Publication Date
8-2016
Source Publication Title
AKCE International Journal of Graphs and Combinatorics
Volume
13
Issue
2
Start Page
200
End Page
209
Publisher
Elsevier
Peer Reviewed
1
Copyright
© 2016 Kalasalingam University. Publishing Services by Elsevier B.V.
DOI
10.1016/j.akcej.2016.06.002
Link to Publisher's Edition
https://doi.org/10.1016/j.akcej.2016.06.002
ISSN (print)
09728600
APA Citation
Lau, G., Shiu, W., & Ng, H. (2016). Further results on super graceful labeling of graphs. AKCE International Journal of Graphs and Combinatorics, 13 (2), 200-209. https://doi.org/10.1016/j.akcej.2016.06.002