Chromatic Values of Intuitionistic Fuzzy Directed Hypergraph Colorings
K. K. Myithili1, R. Parvathi2
1K. K. Myithili, Department of Mathematics, Vellalar College for Women, Erode – 638 012, Tamilnadu, India.
2R. Parvathi, Department of Mathematics, Vellalar College for Women, Erode – 638 012, Tamilnadu, India
Manuscript received on January 09, 2016. | Revised Manuscript received on January 21, 2016. | Manuscript published on March 05, 2016. | PP: 32-37 | Volume-6 Issue-1, March 2016. | Retrieval Number: A2797036116/2016©BEIESP
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© The Authors. Published By: Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: A hypergraph is a set V of vertices and a set E of non-empty subsets of V, called hyperedges. Unlike graphs, hypergraphs can perform higher-order interactions in social and communication networks. Directed hypergraphs are much like directed graphs. Colors are used to distinguish the classes. Coloring a hypergraph H must assign atleast two different colors to the vertices of every hyperedge. That is, no edge is monochromatic. In this paper, upper and lower truncation, core aggregate of intuitionistic fuzzy directed hypergraph (IFDHG), conservative K-coloring of IFDHG, chromatic values of intuitionistic fuzzy colorings, elementary center of intuitionistic fuzzy coloring, f-chromatic value of intuitionistic fuzzy coloring, intersecting IFDHG, K-intersecting IFDHG, strongly intersecting IFDHG were studied. Also it has been proved that IFDHG H is strongly intersecting if and only if it is K-intersecting.
Keywords: Core aggregate of IFDHG, intuitionistic fuzzy colorings (IFC), elementary center, f -chromatic value of IFC, intersecting IFDHG, K-intersecting, strongly intersecting IFDHG.