Ryan, Joe (2009) *Exclusive sum labeling of graphs: a survey.* AKCE International Journal of Graphs and Combinatorics, 6 (1). pp. 113-126.

## Abstract

All sum graphs are disconnected. In order for a connected graph to bear a sum labeling, the graph is considered in conjunction with a number of isolated vertices, the labels of which complete the sum labeling for the disjoint union. The smallest number of isolated vertices that must be added to a graph H to achieve a sum graph is called the sum number of H; it is denoted by Ï�(H). A sum labeling which realizes Hâ�ªKÏ�(G) as a sum graph is called an optimal sum labeling of H. In this paper we survey a new type of labeling based on summation, the exclusive sum labeling. A sum labeling L is called exclusive sum labeling with respect to a subgraph H of G if L is a sum labeling of G where H contains no working vertex. The exclusive sum number Ïµ(H) of a graph H is the smallest number r such that there exists an exclusive sum labeling L which realizes Hâ�ªKr as a sum graph. A labeling L is an optimal exclusive sum labeling of a graph H if L is a sum labeling of Hâ�ªKÏµ(H) and H contains no working vertex.

Item Type: | Article |
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Uncontrolled Keywords: | sum graphs, sum number, optimal sum labeling, exclusive sum labeling, exclusive sum number, optimal exclusive sum labeling |

Subjects: | UNSPECIFIED |

Faculty: | UNSPECIFIED |

Depositing User: | Dr David Allingham |

Date Deposited: | 28 Sep 2012 12:05 |

Last Modified: | 28 Sep 2012 12:05 |

URI: | https://docserver.carma.newcastle.edu.au/id/eprint/1202 |

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