3.24 New Ideas For Setting of Neutrosophic n-SuperHyperGraph

3. Neutrosophic Hypergraphs

(a) : The notions of dominating are applied. (i) : n1 neutrosophic-dominates every vertex from the set of vertices {n7, n8, n9, n2, n3}. n4 neutrosophic-dominates every vertex from the set of vertices {n6, n5, n3}. n4 doesn’t neutrosophic-dominate every vertex from the set of vertices {n1, n2, n7, n8, n9}. (ii) : {n1, n3} is neutrosophic-coloring set but {n1, n4} is optimalneutrosophic-dominating set. (iii) : (1.53, 1.22, 0.71) is optimal-neutrosophic-dominating number. (b) : The notions of resolving are applied. (i) : n1 neutrosophic-resolves two vertices n4 and n6. (ii) : V \ {n1, n4} is neutrosophic-resolves set but V \ {n2, n4, n9} is optimal-neutrosophic-resolving set. (iii) : (5, 94, 6.36, 3.3) is optimal-neutrosophic-resolving number. (c) : The notions of coloring are applied. (i) : n1 neutrosophic-colors every vertex from the set of vertices {n7, n8, n9, n2, n3}. n4 neutrosophic-colors every vertex from the set of vertices {n6, n5, n3}. n4 doesn’t neutrosophic-dominate every vertex from the set of vertices {n1, n2, n7, n8, n9}. (ii) : {n1, n5, n7, n8, n9, n6, n4} is neutrosophic-coloring set but {n1, n5, n7, n8, n2, n4} is optimal-neutrosophic-coloring set. (iii) : (5.24, 4.8, 2.82) is optimal-neutrosophic-coloring number.

3.11 Open Problems

The three notions of coloring, resolving and dominating are introduced on neutrosophic hypergraphs. Thus, Question 3.11.1. Is it possible to use other types neutrosophic hyperedges to define different types of coloring, resolving and dominating on neutrosophic hypergraphs? Question 3.11.2. Are existed some connections amid the coloring, resolving and dominating inside this concept and external connections with other types of coloring, resolving and dominating on neutrosophic hypergraphs? Question 3.11.3. Is it possible to construct some classes on neutrosophic hypergraphs which have “nice” behavior? Question 3.11.4. Which applications do make an independent study to apply these three types coloring, resolving and dominating on neutrosophic hypergraphs? Problem 3.11.5. Which parameters are related to this parameter? Problem 3.11.6. Which approaches do work to construct applications to create independent study? Problem 3.11.7. Which approaches do work to construct definitions which use al l three definitions and the relations amid them instead of separate definitions to create independent study?

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