FUZZY INTERSECTION GRAPHS OF FUZZY SEMIGROUPS

M. K. Sen (), G. Chowdhury and D. S. Malik ()
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M. K. Sen: Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata-700019, India
G. Chowdhury: Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata-700019, India
D. S. Malik: Department of Mathematics, Creighton University, Omaha, NE-68178, USA

New Mathematics and Natural Computation (NMNC), 2006, vol. 02, issue 01, 1-10

Abstract: LetSbe a semigroup. This paper studies the intersection graphs of fuzzy semigroups. It is shown that the fuzzy intersection graphInt(G(S)), ofS, is complete if and only ifSis power joined. IfΓ(S)denotes the set of all fuzzy right ideals ofS, then the fuzzy intersection graphInt(Γ(S))is complete if and only ifSis fuzzy right uniform. Moreover, it is shown thatInt(Γ(S))is chordal if and only if fora,b,c,d ∈ S, some pair from{a,b,c,d}has a right common multiple property. It is also shown that ifInt(G(S))is complete andShas the acc on subsemigroups, thenSis cyclic.

Keywords: Fuzzy subset; fuzzy graph; fuzzy intersection graph; fuzzy subsemigroup (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1142/S179300570600035X

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