Advances and Applications in Discrete Mathematics
Volume 16, Issue 2, Pages 135 - 160
(October 2015) http://dx.doi.org/10.17654/AADMOct2015_135_160 |
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3-UNIFORM HYPERGRAPHS OF RIGHT TERNARY NEAR-RINGS AND EXISTENCE OF BIBDs
A. Uma Maheswari and C. Meera
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Abstract: A right ternary near-ring (RTNR) is an algebraic system which is a group under binary addition and a ternary semigroup under ternary product satisfying the right distributive law. A 3-uniform hypergraph is a hypergraph in which all of its hyperedges are of size 3. In this paper, a 3-uniform hypergraph of an RTNR ‘N’, denoted by is defined. In a zero-symmetric RTNR, some of the properties of are proved. As a special case, is studied in depth. The3-uniform friendship hypergraphs are associated to RTNR in which the ternary product of three distinct elements is zero. The hyperedges of these 3-uniform friendship hypergraphs are treated as blocks and it is shown that the 3-uniform friendship hypergraphs of are balanced incomplete block designs (BIBDs). |
Keywords and phrases: RTNR, 3-uniform hypergraph, 3-uniform friendship hypergraph, BIBD, zero-symmetric RTNR. |
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