A directed graph associated with a $T_0$-quasi-metric space

Document Type : Workshop on Graphs, Topology and Topological Groups, Cape Town, South Africa


1 The Department of Mathematics and Applied Mathematics , University of Cape Town - South Africa

2 Department of Mathematics, Faculty of Science, Hacettepe University, Beytepe -Ankara


Given a $T_0$-quasi-metric space we associate a directed graph with it and study some properties of the related directed graph. The present work complements and refines earlier work in the field in which the symmetry graph of a $T_0$-quasi-metric space was studied.


Main Subjects

[1] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, North-Holland, New York, Fifth Printing, 1982.
[2] M. Charikar, K. Makarychev and Y. Makarychev, Directed metrics and directed graph partitioning problems, Proc. Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms, ACM, New York, 2006 51–60.
[3] S¸. Cobza¸s, Functional Analysis in Asymmetric Normed Spaces, Frontiers in Mathematics, Springer, Basel, 2013.
[4] J. Ferrer, V. Gregori and C. Alegre, Quasi-uniform structures in linear lattices, Rocky Mountain J. Math., 23 no. 5 (1993) 877–884.
[5] E. Kemajou, H.-P. A K¨unzi and O. O. Otafudu, The Isbell-hull of a di-space, Topology Appl., 159 (2012) 2463–2475.
[6] H. -P. A. K¨unzi and V. Vajner, Weighted quasi-metrics, Ann. New York Acad. Sci., 728 (1994) 64–77.
[7] N. Javanshir and F. Yıldız, Symmetrically connected and antisymmetrically connected T0-quasi-metric extensions, Topology Appl., 276 (2020) 18 pp.
[8] I. L. Reilly and M. K. Vamanamurthy, On oriented metric spaces, Math. Slovaca, 34 no. 3 (1984) 299–305.
[9] F. M. Solofomananirina Tiantsoa and H. -P. A. K¨unzi, Splitting ultra-metrics by T0-ultra-quasi-metrics, Topology Appl., 240 (2018) 21–34.
[10] F. Yıldız and H.-P.A. K¨unzi, Symmetric connectedness in T0-quasi-metric spaces, Bull. Belgian Math Soc., 26 no. 5 (2019) 659–679. 
Volume 11, Issue 3 - Serial Number 3
Introduction to the Proceedings of WGTTG2021
September 2022
Pages 237-254
  • Receive Date: 24 June 2021
  • Revise Date: 04 February 2022
  • Accept Date: 06 February 2022
  • Published Online: 01 September 2022