Browsing by Author "Divya A"

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    AN ALEXANDAN ALEXANDROFFBITOPOLOGICAL SPACE ON UNDIRECTED GRAPHSROAN ALEXANDROFFBITOPOLOGICAL SPACE ON UNDIRECTED GRAPHSFFBITOPOLOGICAL SPACE ON UNDIRECTED GRAPHS
    (Centre of scientific innovation and research publication, 2019-07) Sasikala D; Divya A
    All nodes (vertices) has finitely many adjacent nodes(vertices) in graph G = (V, E) is calledlocally finite graph, where V is referred as vertex (node) set and E is referred as edge (arc) set.Alexandroff spaces became much more important field because of their use in digital topology.Alexandroff space is a topological space, in which arbitrary intersection of open sets is open (orarbitrary union of closed sets is closed) equivalently, we say that each singleton has minimalneighborhood base. The bitopological spaces that is the triple (A, τ1, τ2 ) of a collection A with two(arbitrary) topologies τ1and τ2on A. In this paper, we mean by a bitopologicalspace(V,τG,τIG) is anAlexandroffbitopological space, satisfy the stronger condition namely, arbitrary intersection ofmembers of SG and SIG are open in τG and τIG respectively on V, whereSG is the sub basis for agraphic topology τG and SIG is the sub basis for a incident topology τIG. Latter, we investigate someproperties and characterization of this topological spaces. In particular, the separation axioms arestudied. Our goal is to consider the fundamentalsteps toward analyzing some properties of locallyfundamental steps toward analyzing some properties of locallyfinite graphs by their corresponding topology.
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    AN ALEXANDROFF TOPOLOGICAL SPACE ON THEVERTEX SET OF SUM CORDIAL GRAPHS
    (Institute of Advanced Scientific Research, 2019) Sasikala D; Divya A
    The goal of the article is to introduce cordial Alexandroff topological space on sum cordial graphs. Weinvestigate some properties of cordial Alexandroff topological space and additionally we have a tendency to provesome graphs which does not admits cordial alexandroff topological space
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    BEHAVIOR OF OPEN SETS IN BI-ALEXANDROFF TOPOLOGICAL SPACE
    (University Press, 2019) Sasikala D; Divya A
    The goal of this paper is to establish, the properties of which exhibit the characterization of a j-open set in bi-Alexandroff topological space and some properties of j-open set are analyzed. Also we have studied the notion of j-bi-continuous function in bi-Alexandroff topological space.
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    DIVISOR CORDIAL GRAPHS CONTAINING AN ALEXANDROFF TOPOLOGICALSPACE
    (Institute of Applied & computations, 2019-03) Sasikala D; Divya A
    The aim of this article is to introduce a new approach of applying the Alexandroff topological space on divisor cordial graphs. Our motivation is towards giving fundamental concepts relating divisor cordial graphs bytheir corresponding topology. Some properties and characterization relating to these spaces are discussed.
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    NECESSARY OR SUFFICIENT CONDITION FOR ALEXANDROFF TOPOLOGICAL SPACES TO BE CORDIAL GRAPHIC (Article)
    (Elsevier B.V., 2024-12) Divya A; Ramya K; Sasikala D
    In this paper, we explore the property of being a cordial graphic and establish that it corresponds to an Alexandroff topological space. We analyze how the characteristics of cordial graphs align with the principles of Alexandroff topology and provide insights into their topological structure.
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    THE ROLE OF INTERIOR AND CLOSURE OPERATOR IN MEDICAL APPLICATIONS
    (Journal of Applied and Engineering Mathematics, 2022) Sasikala D; Divya A; Jafari S
    In this paper, we consider the interior and closure operator as topological tools to apply in divisor cordial labeling. We investigate the properties related to the path with certain examples in a divisor cordial graphic topology. This concept is utilized in human blood circulation path and the results are analyzed.