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Fuzzy Intersection Graphs Of Fuzzy Semigroups

Author

Listed:
  • 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)

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.

Suggested Citation

  • M. K. Sen & G. Chowdhury & D. S. Malik, 2006. "Fuzzy Intersection Graphs Of Fuzzy Semigroups," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 2(01), pages 1-10.
    • Handle: RePEc:wsi:nmncxx:v:02:y:2006:i:01:n:s179300570600035x
    DOI: 10.1142/S179300570600035X
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