TY - JOUR
T1 - Further results on super graceful labeling of graphs
AU - Lau, Gee Choon
AU - Shiu, Wai Chee
AU - Ng, Ho Kuen
N1 - Publisher Copyright:
© 2016 Kalasalingam University
PY - 2016/8/1
Y1 - 2016/8/1
N2 - 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.
AB - 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.
KW - Graceful labeling
KW - Super graceful labeling
KW - Tree
UR - http://www.scopus.com/inward/record.url?scp=84977644711&partnerID=8YFLogxK
U2 - 10.1016/j.akcej.2016.06.002
DO - 10.1016/j.akcej.2016.06.002
M3 - Journal article
AN - SCOPUS:84977644711
SN - 0972-8600
VL - 13
SP - 200
EP - 209
JO - AKCE International Journal of Graphs and Combinatorics
JF - AKCE International Journal of Graphs and Combinatorics
IS - 2
ER -