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A study on graph topology | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 9، دوره 8، شماره 2، شهریور 2023، صفحه 397-409 اصل مقاله (372.44 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2022.27399.1253 | ||
| نویسندگان | ||
| Achu Aniyan1؛ Sudev Naduvath* 2 | ||
| 1Department of Mathematics, Christ University, Bangalore, India. | ||
| 2Christ University, Bangalore, India. | ||
| چکیده | ||
| The concept of topology defined on a set can be extended to the field of graph theory by defining the notion of graph topologies on graphs where we consider a collection of subgraphs of a graph $G$ in such a way that this collection satisfies the three conditions stated similarly to that of the three axioms of point-set topology. This paper discusses an introduction and basic concepts to the graph topology. A subgraph of $G$ is said to be open if it is in the graph topology $\mathscr{T}_G$. The paper also introduces the concept of the closed graph and the closure of graph topology in graph topological space using the ideas of decomposition-complement and neighborhood-complement. | ||
| کلیدواژهها | ||
| Graph topology؛ graph topological space؛ $sT$-interior؛ $sT$-neighbourhood | ||
| مراجع | ||
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[6] K.D. Joshi, Introduction to General Topology, New Age International, 1983.
[7] W.B.V. Kandasamy and F. Smarandache, Strong Neutrosophic Graphs and Subgraph Topological Subspaces, EuropaNova, 2016.
[8] K. Karunakaran, Topics in graph theory topological approach, Ph.D. thesis, University of Kerala, 2007.
[9] J.L. Kelley, General Topology, Courier Dover Publications, 2017.
[10] J. Munkres, Topology, Pearson Education, 2014.
[11] A.E. Wegner, Subgraph covers: an information-theoretic approach to motif analysis in networks, Physical Review X 4 (2014), no. 4, 041026.
[12] D.B. West, Introduction to Graph Theory, vol. 2, Prentice-Hall of India, New Delhi, 2001. | ||
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