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2010 | 30 | 4 | 671-685
Tytuł artykułu

n-ary transit functions in graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
n-ary transit functions are introduced as a generalization of binary (2-ary) transit functions. We show that they can be associated with convexities in natural way and discuss the Steiner convexity as a natural n-ary generalization of geodesicaly convexity. Furthermore, we generalize the betweenness axioms to n-ary transit functions and discuss the connectivity conditions for underlying hypergraph. Also n-ary all paths transit function is considered.
Słowa kluczowe
Wydawca
Rocznik
Tom
30
Numer
4
Strony
671-685
Opis fizyczny
Daty
wydano
2010
otrzymano
2009-11-11
zaakceptowano
2010-03-02
Twórcy
  • Department of Futures Studies, University of Kerala, Trivandrum, India
  • Department of Futures Studies, University of Kerala, Trivandrum, India
  • Institute of Mathematics and Physics, FEECS, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia
  • Department of Mathematics, Government College, Chittur, Palakkad - 678 104, India
Bibliografia
  • [1] B. Bresar, M. Changat, J. Mathews, I. Peterin, P.G. Narasimha-Shenoi and A. Tepeh Horvat, Steiner intervals, geodesic intervals, and betweenness, Discrete Math. 309 (2009) 6114-6125, doi: 10.1016/j.disc.2009.05.022.
  • [2] M. Changat, S. Klavžar and H.M. Mulder, The All-Paths Transit Function of a Graph, Czechoslovak Math. J. 51 (126) (2001) 439-448.
  • [3] M. Changat and J. Mathew, Induced path transit function, monotone and Peano axioms, Discrete Math. 286 (2004) 185-194, doi: 10.1016/j.disc.2004.02.017.
  • [4] M. Changat and J. Mathew, Characterizations of J-monotone graphs, in: Convexity in Discrete Structures (M. Changat, S. Klavžar, H.M. Mulder, A. Vijayakumar, eds.), Lecture Notes Ser. 5, Ramanujan Math. Soc. (2008) 47-55.
  • [5] M. Changat, J. Mathew and H.M. Mulder, Induced path function, betweenness and monotonicity, Discrete Appl. Math. 158 (2010) 426-433, doi: 10.1016/j.dam.2009.10.004.
  • [6] M. Changat, J. Mathew and H.M. Mulder, Induced path transit function, betweenness and monotonicity, Elect. Notes Discrete Math. 15 (2003).
  • [7] M. Changat, H.M. Mulder and G. Sierksma, Convexities Related to Path Properties on Graphs, Discrete Math. 290 (2005) 117-131, doi: 10.1016/j.disc.2003.07.014.
  • [8] M. Changat, P.G. Narasimha-Shenoi and I.M. Pelayo, The longest path transit function and its betweenness, to appear in Util. Math.
  • [9] P. Duchet, Convexity in combinatorial structures, Rend. Circ. Mat. Palermo (2) Suppl. 14 (1987) 261-293.
  • [10] P. Duchet, Convex sets in graphs II. Minimal path convexity, J. Combin. Theory (B) 44 (1988) 307-316, doi: 10.1016/0095-8956(88)90039-1.
  • [11] P. Duchet, Discrete convexity: retractions, morphisms and partition problem, in: Proceedings of the conference on graph connections, India, (1998), Allied Publishers, New Delhi, 10-18.
  • [12] P. Hall, On representation of subsets, J. Lon. Mat. Sc. 10 (1935) 26-30, doi: 10.1112/jlms/s1-10.37.26.
  • [13] M.A. Morgana and H.M. Mulder, The induced path convexity, betweenness and svelte graphs, Discrete Math. 254 (2002) 349-370, doi: 10.1016/S0012-365X(01)00296-5.
  • [14] H.M. Mulder, The Interval Function of a Graph. Mathematical Centre Tracts 132, Mathematisch Centrum (Amsterdam, 1980).
  • [15] H.M. Mulder, Transit functions on graphs (and posets), in: Convexity in Discrete Structures (M. Changat, S. Klavžar, H.M. Mulder, A. Vijayakumar, eds.), Lecture Notes Ser. 5, Ramanujan Math. Soc. (2008) 117-130.
  • [16] L. Nebeský, A characterization of the interval function of a connected graph, Czechoslovak Math. J. 44(119) (1994) 173-178.
  • [17] L. Nebeský, A Characterization of the interval function of a (finite or infinite) connected graph, Czechoslovak Math. J. 51(126) (2001) 635-642.
  • [18] E. Sampathkumar, Convex sets in graphs, Indian J. Pure Appl. Math. 15 (1984) 1065-1071.
  • [19] M.L.J. van de Vel, Theory of Convex Structures (North Holland, Amsterdam, 1993).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1522
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