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Open accessJournal ArticleDOI: 10.1088/1757-899X/263/4/042129

Planar graph characterization of NDSS graphs

01 Nov 2017-Vol. 263, Iss: 4, pp 042129
Abstract: Planar graph characterization is always of interest due to its complexity in characterization. In this paper, we obtain a necessary and sufficient condition for a graph to be NDSS and hence characterize the planarity and outer – planarity of its complement .

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Topics: Planarity testing (67%), Planar graph (66%)
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Open accessJournal ArticleDOI: 10.14419/IJET.V7I4.10.26656
A. Elakkiya1, M. Yamuna1Institutions (1)
Abstract: A uniquely colorable graph G whose chromatic partition contains atleast one g - set is termed as a g - uniquely colorable graph. In this paper, we provide necessary and sufficient condition for and G* to be g - uniquely colorable whenever G g- uniquely colorable and also provide constructive characterization to show that whenever G is g- uniquely colorable such that |P | ³ 2, G can be both planarand non planar.

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Topics: Uniquely colorable graph (79%)

Book ChapterDOI: 10.1007/978-3-030-01123-9_45
M. Yamuna1, A. Elakkiya1Institutions (1)
01 Jan 2019-
Abstract: A uniquely colorable graph G whose chromatic partition contains at least one γ-set is termed as a γ-uniquely colorable graph. We characterize the planarity of these graphs using the domination number of G.

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Topics: Uniquely colorable graph (80%), Planar graph (71%), Planarity testing (65%) ...read more
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Open accessJournal ArticleDOI: 10.1155/S016117127900020X
Abstract: We investigate the conditions under which both a graph G and its complement G¯ possess a specified property. In particular, we characterize all graphs G for which G and G¯ both (a) have connectivity one, (b) have line-connectivity one, (c) are 2-connected, (d) are forests, (e) are bipartite, (f) are outerplanar and (g) are eulerian. The proofs are elementary but amusing.

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Topics: Complement graph (62%), Pathwidth (58%), Bipartite graph (56%) ...read more

25 Citations

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No. of citations received by the Paper in previous years
YearCitations
20191
20181