Table of Contents
International Journal of Combinatorics
Volume 2015 (2015), Article ID 528083, 5 pages
http://dx.doi.org/10.1155/2015/528083
Research Article

Starter Labelling of -Windmill Graphs with Small Defects

Department of Mathematics and Statistics, Memorial University of Newfoundland and Labrador, St. John’s, NL, Canada A1C 5S7

Received 25 March 2015; Accepted 9 July 2015

Academic Editor: Chris A. Rodger

Copyright © 2015 Farej Omer and Nabil Shalaby. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A graph on vertices can be starter-labelled, if the vertices can be given labels from the nonzero elements of the additive group such that each label , either or , is assigned to exactly two vertices and the two vertices are separated by either edges or edges, respectively. Mendelsohn and Shalaby have introduced Skolem-labelled graphs and determined the conditions of -windmills to be Skolem-labelled. In this paper, we introduce starter-labelled graphs and obtain necessary and sufficient conditions for starter and minimum hooked starter labelling of all -windmills.