On topological spaces generated by simple undirected graphs

Sarı, Hatice Kübra; Kopuzlu, Abdullah

doi:10.3934/math.2020355

Cited by 7 publications

(2 citation statements)

References 3 publications

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“…We demonstrate that every basic graph may generate a topology. Obtain the topological space by converting the simple connected graph [12,13]. In this article, we discuss a new method for generating a topology on the graph using a new method, which is converting the graph into an adjacent matrix that represents the correlation of each vertex with the rest of the vertices and, depending on the shape of the matrix and the rows it contains, we get a set for each rows containing only the vertices associated with that header then we col-lect these rows according to the sites in the set that we got.…”

Section: Introductionmentioning

confidence: 99%

On Finite Topological Spaces Generated by Connected Simple Graphs

Noor Nouman

2024

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In this paper, we investigate topologies produced by simple connected graphs. In particular, we will present the type of relations on the vertices set. It is converted to an adjacent matrix and through this matrix, whose elements represent the relationship between each vertex to the rest of the vertices adjacent to it, where sets are produced through which they represent the basis for topology. On the graph is the vertex set.

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Section: Introductionmentioning

confidence: 99%

On Finite Topological Spaces Generated by Connected Simple Graphs

Noor Nouman

2024

cana

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“…In 2013, SNF Al-khafaji [7] have constructed a topology on graphs and a topology on subgraphs, and in 2018, KA Abdu [1] have constructed applying the topology on digraphs by associate two topologies with the set of edges of any directed graph, called compatible and incompatible edges topologies. Various relationships were used by researchers, as some researchers presented the relationships that connect the topological space with the graph by means of vertices [6,10,11].…”

Section: Introductionmentioning

confidence: 99%

On topological spaces generated by graphs and vice versa

Ibraheem

Nagim

2021

J. Al-Qadisiyah Comp. Sci. Math.

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The relationship between Graph Theory and Topological Space has recently developed greatly , as researchers have been able to find solutions to some problems in daily life by transforming the problem into a graph and then generating a topological space and thus facilita- ting reading the problem and solving it. The researchers also studied the generation of graph from topological spaces.In this article we will present two types of relations on the edges set that generate topolog- ical spaces, and we will discuss some properties of this topology, and we will study discuss the method of returning from the topological space to the graphs through using previous relationships.

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