- Title
- Exclusive sum labeling of graphs: a survey
- Creator
- Ryan, Joe
- Relation
- AKCE International Journal of Graphs and Combinatorics Vol. 6, Issue 1, p. 113-126
- Relation
- http://www.akcejournal.org/contents/vol6no1/vol6_no1_13.htm
- Publisher
- Kalasalingam University
- Resource Type
- journal article
- Date
- 2009
- Description
- 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 σ(H). A sum labeling which realizes H∪Kσ(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 ϵ(H) of a graph H is the smallest number r such that there exists an exclusive sum labeling L which realizes H∪Kr as a sum graph. A labeling L is an optimal exclusive sum labeling of a graph H if L is a sum labeling of H∪Kϵ(H) and H contains no working vertex.
- Subject
- sum graphs; sum number; optimal sum labeling; exclusive sum labeling; exclusive sum number; optimal exclusive sum labeling
- Identifier
- http://hdl.handle.net/1959.13/808825
- Identifier
- uon:7763
- Identifier
- ISSN:0972-8600
- Language
- eng
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