Advances and Applications in Discrete Mathematics
Volume 16, Issue 1, Pages 41 - 50
(July 2015) http://dx.doi.org/10.17654/AADMJul2015_041_050 |
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DISTANCE COMPACTIBLE SET LABELED GRAPHS AND FRIENDSHIP HYPERGRAPHS
K. A. Germina
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Abstract: A hypergraph is a pair where is the set of vertices of and is a subset of the power set of V without empty set, each element in denoted as an edge. The number of vertices n is the order of the hypergraph. If each edge in contains exactly r vertices, then the hypergraph is r-uniform. A distance compatible set labeling (dcsl) of a graph G is an injective set- assignment X a nonempty ground set such that the corresponding induced function defined by the symmetric difference function satisfies for each pair of distinct where is the distance between u and v and are constants. A dcsl f of G is k-uniform if all the are equal to k and if G admits such a dcsl, then G is called a k-uniform dcsl graph. This paper is the construction of 3-uniform friendship hypergraphs from 1-uniform dcsl graphs. |
Keywords and phrases: hypergraph, dcsl graphs, 1-uniform dcsl graphs, Steiner triple system, 3-uniform hypergraphs, friendship hypergraphs. |
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