Planar and Non Planar Construction of - Uniquely Colorable Graph
A. Elakkiya,M. Yamuna +1 more
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A uniquely colorable graph G whose chromatic partition contains atleast one g-set is termed as a g-uniquely-coloring graph as discussed by the authors, and the necessary and sufficient condition for and G* to be g -uniquely colorable whenever G G is g-colorable such that |P | ³ 2, G can be both planar and nonplanar.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. read more
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Fundamentals of domination in graphs
TL;DR: Bounds on the domination number domination, independence and irredundance efficiency, redundancy and the duals changing and unchanging domination conditions on the dominating set varieties of domination multiproperty and multiset parameters sums and products of parameters dominating functions frameworks for domination domination complexity and algorithms are presented.
Journal ArticleDOI
Uniquely colorable graphs
TL;DR: If G is a graph of order n that has a k-coloring in which the subgraph induced by the union of any two color classes is connected then δ(G)>(1−(1/(k−1))) n implies that G is uniquely k-colorable.
Journal ArticleDOI
On the Maximum Number of Dominating Classes in Graph Coloring
TL;DR: In this paper, the dominating-c-color number of a graph G is investigated, i.e., the maximum number of color classes that are also dominating when G is colored using colors.
Journal ArticleDOI
Planar graph characterization of γ - Uniquely colorable graphs
M Yamuna,A. Elakkiya +1 more
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Planar graph characterization of NDSS graphs
M Yamuna,A. Elakkiya +1 more
TL;DR: This paper obtains a necessary and sufficient condition for a graph to be NDSS and hence characterize the planarity and outer – planarity of its complement.