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Domination in different graphs
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| Author:
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K.MYTHILY , S.KALAIVANI, P.ELUMALAI , P.THARANIYA
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| Abstract:
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In this paper analyses the concept of domination and its characteristics in graph theory. Here the concept of Domination, Maximum Dominating Set and Maximal Dominating Set as well as the concept of Independent set, Maximum Independent set and Maximal Independent Set are discussed in further. Dominating set is the collection of possible non-touching vertices through the single edge. Maximum Dominating set consist maximum number of possible non-touching vertices in the given graph. Maximal Domination Set consist minimum number of possible non-touching vertices which is adjacent with all the edges in the graph. Various types of Graphs, Structure and their properties also have to be discussed. Major part of this paper considers the cardinality calculation of Maximum and Maximal Dominating sets in the various graphs. After calculation, it derived a general formula for the calculation of Maximum Dominating cardinality and Maximal Dominating Cardinality. The calculation values should be representing in table format.
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| Keyword:
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Domination, Independent set, Graph, Vertex Degrees, Path, Cycle.
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| EOI:
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-
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| DOI:
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https://doi.org/10.31838/ijpr/2021.13.01.054
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| Download:
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