Further results on super graceful labeling of graphs

Gee Choon Lau*, Wai Chee SHIU, Ho Kuen Ng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)200-209
Number of pages10
JournalAKCE International Journal of Graphs and Combinatorics
Volume13
Issue number2
DOIs
Publication statusPublished - 1 Aug 2016

Scopus Subject Areas

  • Discrete Mathematics and Combinatorics

User-Defined Keywords

  • Graceful labeling
  • Super graceful labeling
  • Tree

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