Some properties of the topological spaces generated from the simple undirected graphs

Hatice Kübra Sarı

Some properties of the topological spaces generated from the simple undirected graphs

Abstract

Graph theory, which is used effectively in many fields from science to liberal arts, has very important place in our lives. As a result of this, the topological structure of the graphs is stud-ied by many researchers. In this paper, we investigate the topological spaces generated by the graphs. The states of being an accumulation point and an interior point of a point in these spaces are examined. It is defined that relative topology on a subgraph of a graph. It is shown that this topology is different from the topology generated by this subgraph. Moreover, using the minimal adjacencies of vertices set of a graph, necessary and sufficient conditions for be-ing 𝑇0 -space, 𝑇1-space and Hausdorff space of the topological space generated from this graph are presented. This enables to examine whether the topological space is 𝑇0, 𝑇1 and Hausdorff without obtaining the topology generated from the graph.

Keywords

References

REFERENCES
[1] Abdu KA, Kılıcman A. Topologies on the edges set of directed graphs. Int J Math Anal 2018:12;71-84.[CrossRef]
[2] Amiri SM, Jafarzadeh A, Khatibzadeh H. An Alexandroff topology on graphs. Bull Iran Math Soc 2013;39:647-662.
[3] Bondy JA, Murty USR. Graph Theory. 1st ed. Berlin: Springer; 2008. [CrossRef]
[4] Euler L. Solutio problematis ad geometriam situs pertinentis. Commentarii Academiae Scientiarum Imperi- alis Petropolitanae 1736;8:128-140.
[5] Lipschutz S. Schaum's Outline of Theory and Problems of General Topology. 1st ed. New York: Mcgraw-Hill Book Company; 1965.
[6] Sarı HK, Kopuzlu A. A note on a binary relation corresponding to a bipartite graph. ITM Web Conf 2018;22:01039. [CrossRef]
[7] Sarı HK, Kopuzlu A. On topological spaces gener-ated by simple undirected graphs. Aims Mathematics 2020;5:5541-5550. [CrossRef]

Details

Primary Language

English

Subjects

Empirical Software Engineering

Journal Section

Research Article

Authors

Hatice Kübra Sarı ^* This is me
0000-0001-5110-1256
Türkiye

Publication Date

April 30, 2023

Submission Date

April 14, 2021

Acceptance Date

July 5, 2021

Published in Issue

Year 2023 Volume: 41 Number: 2

IZ

https://izlik.org/JA23WJ72FM

Cite

RIS / Bibtex

APA

Sarı, H. K. (2023). Some properties of the topological spaces generated from the simple undirected graphs. Sigma Journal of Engineering and Natural Sciences, 41(2), 266-270. https://izlik.org/JA23WJ72FM

AMA

1.Sarı HK. Some properties of the topological spaces generated from the simple undirected graphs. SIGMA. 2023;41(2):266-270. https://izlik.org/JA23WJ72FM

Chicago

Sarı Hatice Kübra. 2023. “Some Properties of the Topological Spaces Generated from the Simple Undirected Graphs”. Sigma Journal of Engineering and Natural Sciences 41 (2): 266-70. https://izlik.org/JA23WJ72FM.

EndNote

Sarı HK (April 1, 2023) Some properties of the topological spaces generated from the simple undirected graphs. Sigma Journal of Engineering and Natural Sciences 41 2 266–270.

IEEE

[1]H. K. Sarı, “Some properties of the topological spaces generated from the simple undirected graphs”, SIGMA, vol. 41, no. 2, pp. 266–270, Apr. 2023, [Online]. Available: https://izlik.org/JA23WJ72FM

ISNAD

Sarı Hatice Kübra. “Some Properties of the Topological Spaces Generated from the Simple Undirected Graphs”. Sigma Journal of Engineering and Natural Sciences 41/2 (April 1, 2023): 266-270. https://izlik.org/JA23WJ72FM.

JAMA

1.Sarı HK. Some properties of the topological spaces generated from the simple undirected graphs. SIGMA. 2023;41:266–270.

MLA

Sarı Hatice Kübra. “Some Properties of the Topological Spaces Generated from the Simple Undirected Graphs”. Sigma Journal of Engineering and Natural Sciences, vol. 41, no. 2, Apr. 2023, pp. 266-70, https://izlik.org/JA23WJ72FM.

Vancouver

1.Hatice Kübra Sarı. Some properties of the topological spaces generated from the simple undirected graphs. SIGMA [Internet]. 2023 Apr. 1;41(2):266-70. Available from: https://izlik.org/JA23WJ72FM