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

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Included in

Mathematics Commons

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