Let G = (V,E) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an elementary step toward investigation of some properties of locally finite graphs by their corresponding topology which we introduce in this paper.
Jafarian Amiri, S. M., Jafarzadeh, A., & Khatibzadeh, H. (2013). An Alexandroff topology on graphs. Bulletin of the Iranian Mathematical Society, 39(4), 647-662.
MLA
Jafarian Amiri, S. M., Jafarzadeh, A., & Khatibzadeh, H. "An Alexandroff topology on graphs", Bulletin of the Iranian Mathematical Society, 39, 4, 2013, 647-662.
HARVARD
Jafarian Amiri S. M., Jafarzadeh A., Khatibzadeh H. (2013). 'An Alexandroff topology on graphs', Bulletin of the Iranian Mathematical Society, 39(4), pp. 647-662.
CHICAGO
S. M. Jafarian Amiri, A. Jafarzadeh & H. Khatibzadeh, "An Alexandroff topology on graphs," Bulletin of the Iranian Mathematical Society, 39 4 (2013): 647-662,
VANCOUVER
Jafarian Amiri S. M., Jafarzadeh A., Khatibzadeh H. An Alexandroff topology on graphs. BIMS. 2013;39(4):647-662.
