Volume 18, Issue 2, pp 232--241
Publication Date: 2018-02-01
Khalid Abdulkalek Abdu
- Department of Mathematics, University Putra Malaysia (UPM), 4300 Serdang, Selangor, Malaysia and Department of Accounting, Al-Iraqia University, Adhmia, Baghdad, Iraq
Adem Kilicman - Department of Mathematics, University Putra Malaysia (UPM), 4300 Serdang, Selangor, Malaysia
The aim of this article is to associate a bitopological space with every locally finite graph G (a graph in which every vertex is adjacent with finite number of edges). Then some properties of this bitopological space were investigated. After that, connectedness and dense subsets were discussed. Giving a fundamental step toward studying some properties of locally finite graphs by their corresponding bitopological spaces is our motivation.
Locally finite graph, undirected graphs, bitopological spaces
 E. V. Baby Girija, R. Pilakkat, Bitopological spaces associated with digraphs, South Asian J. Math., 3 (2013), 56–66.
 A. Bretto, Digital topologies on graphs, Springer-Verlag, Berlin, (2007).
 B. P. Dvalishvili, Bitopological spaces: theory, relations with generalized algebraic structures, and applications, Elsevier, Amesterdam, (2005).
 S. M. Jafarian Amiri, A. Jafarzadeh, H. Khatibzadeh, An Alexandroff topology on graphs, Bull. Iranian Math. Soc., 39 (2013), 647–662.
 A. Kilicman, K. Abdulkalek, Topological spaces associated with simple graphs, (submitted).
 J. M. Moller, General topology, Matematisk Institut, Kobenhavn, (2007).
 M. J. Saegrove, On bitopological spaces, Thesis (Ph.D.), Iowa State University, ProQuest LLC, (1971).
 S. Saha Ray, Graph theory with algorithms and its applications, Springer Publishers, New Delhi, (2013).
 C. Vasudev, Graph theory with applications, New age international, New Delhi, (2006).