A Note On Set-Indexed Graphs
Publication Type:Journal Article
Source:Journal of Discrete Mathematical Sciences and Cryptography, Taru Publications, Volume 18, p.31-40 (2015)
Keywords:Finite set, Graceful graphs, Graph G, Graph theory, Graphic methods, New results, Nonempty subsets, Set-indexed graphs, Set-sequential graphs, Symmetric difference
A set-indexer  of the graph G is an assignment of distinct subsets of a finite set X to the vertices of the graph, where the sets on the edges are obtained as the symmetric differences of the sets assigned to their end vertices which are also distinct. A set-indexer is called a set-sequential if sets on the vertices and edges are distinct and together form the set of all nonempty subsets of X. A set-indexer is called a set-graceful if all the nonempty subsets of X are obtained on the edges. A graph is called set-sequential (set-graceful) if it admits a set-sequential (set-graceful) labeling. The objective of this note is to report some new results, open problems and conjectures in relation to set-indexed graphs. © 2015, © Taru Publications.
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