Document Type : Original Manuscript

Authors

Mathematics Department, Faculty of Basic Science, Khatam-ol-Anbia (PBU) University, Tehran, Iran.

Abstract

In this paper, we introduce a path hyperoperation associated with a hypergraph,
which is an extension of the Corsini’s hyperoperation.
We investigate some related properties and study relations between
the path hyperoperation and hypergraph theory.

Keywords

1. M. I. Ali, Hypergraphs, hypergroupoid and hypergroups, Ital. J. Pure Appl. Math., 8 (2000), 45–48.
2. C. Berge, Graphs and Hypergraphs, North-Holland, New York, 1976.
3. C. Berge, Hypergraphs, North-Holland, Amsterdam, 1989.
4. N. Biggs, Algebraic Graph Theory, Cambridge University Press, New York, 1974.
5. N. Boysen, M. Fliedner, A. Scholl, Assembly line balancing: Joint precedence graphs under high product variety, IIE Transactions, 41 (2009), 183–193.
6. J. Bukchin, E. M. Dar-El, J. Rubinovitz, Mixed model assembly line design in a make-to-order environment, Comput. Ind. Eng., 41 (2001), 405–421.
7. P. Corsini, Binary relations and hypergroupoids, Ital. J. Pure Appl. Math., 7 (2000), 11–18.
8. P. Corsini, Hypergraphs and hypergroups, Algebra Universalis, 35 (1996), 548–555.
9. P. Corsini, Prolegomena of Hypergroups Theory, Aviani Editore, Italy, 1993.
10. P. Corsini, V. Leoreanu, Applications of Hyperstructure Theory, Advances in Mathematics, Kluwer Academic Publishers, Dordrecht, 2003.
11. P. Corsini, V. Leoreanu, Hypergroups and binary relations, Algebra Universalis, 43 (2000), 321–330.
12. I. Cristea, M. Stefanescu, Binary relations and reduced hypergroups, Discrete Math., 308 (2008), 3537–3544.
13. I. Cristea, M. Stefanescu, Hypergroups and n-ary relations, European J. Combin., 31 (2010), 780–789.
14. I. Cristea, M. Stefanescu, C. Anghluta, About the fundamental relations defined on the hypergroupoids associated with binary relations, European J. Combin., 32 (2011), 72–81.
15. M. De Salvo, G. Lo Faro, A new class of hypergroupoids associated to binary relations, J. Mult.-Valued Logic Soft Comput., 9 (2003), 361–375.
16. M. Farshi, B. Davvaz, S. Mirvakili, Degree hypergroupoids associated with hypergraphs, J. Faculty of Sciences and Math, University of Nis, Serbia., 28 (2014), 119–129.
17. M. N. Iradmusa, A. Iranmanesh, The combinatorial and algebraic structure of
the hypergroup associated to a hypergraph, J. Mult.-Valued Logic Soft Comput., 11 (2005), 127–136.
18. A. Kalampakas, S. Spartalis, Path hypergroupoids: Commutativity and graph connectivity, European J. Combin., 44 (2015), 257–264.
19. A. Kalampakas, S. Spartalis, K. Skoulariki, Directed graphs representing isomorphism classes of C-hypergroupoids, Ratio Math., 23 (2012), 51–64.
20. A. Kalampakas, S. Spartalis, A. Tsigkas, The path hyperoperation, J. Anal. Univ. Ovidius Constanta, Ser. Mat., 22 (2014), 141–153.
21. V. Leoreanu and L. Leoreanu, Hypergroups associated with hypergraphs, Ital. J. Pure Appl. Math., 4 (1998), 119–126.
22. V. Leoreanu-Fotea, P. Corsini, A. Iranmanesh, On the sequence of hypergroups and membership functions determined by a hypergraph, J. Mult.-Valued Logic Soft Comput., 14 (2008), 565–577.
23. F. Marty, Sur une généralization de la notion de group, 8th Congress Math. Scandenaves, Stockholm, (1934), 45–49.
24. S. Spartalis, Hypergroupoids obtained from groupoids with binary relations, Ital. J. Pure Appl. Math., 16 (2004), 201–210.
25. S. Spartalis, The hyperoperation relation and the Corsini’s partial or not-partial hypergroupoids (A classification), Ital. J. Pure Appl. Math., 24 (2008), 97–112.
26. S. Spartalis, M. Konstantinidou, A. Taouktsoglou, C-hypergroupoids obtained by special binary relations, Comput. Math. Appl., 59 (2010), 2628–2635.
27. S. Spartalis, C. Mamaloukas, On hyperstructures associated with binary relations, Comput. Math. Appl., 51 (2006), 41–50.