More about edge domination in hyper graph
نویسندگان
چکیده
منابع مشابه
Edge Criticality in Graph Domination
A vertex subset D ⊆ V of a graph G = (V, E) is a dominating set of G if each vertex of G is a member of D or is adjacent to a member of D. The cardinality of a smallest dominating set of G is called the domination number of G and a nonempty graph G is q-critical if q is the smallest number of arbitrary edges of G whose removal fromG necessarily increases the domination number of the resulting g...
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Let G=(V(G),E(G)) be a simple connected graph with vertex set V(G) and edge set E(G). The (first) edge-hyper Wiener index of the graph G is defined as: $$WW_{e}(G)=sum_{{f,g}subseteq E(G)}(d_{e}(f,g|G)+d_{e}^{2}(f,g|G))=frac{1}{2}sum_{fin E(G)}(d_{e}(f|G)+d^{2}_{e}(f|G)),$$ where de(f,g|G) denotes the distance between the edges f=xy and g=uv in E(G) and de(f|G)=∑g€(G)de(f,g|G). In thi...
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The domination number of a graph is the cardinality of a smallest subset of its vertex set with the property that each vertex of the graph is in the subset or adjacent to a vertex in the subset. This graph parameter has been studied extensively since its introduction during the early 1960s and finds application in the generic setting where the vertices of the graph denote physical entities that...
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A subset X of the vertex set of a graph G is a secure dominating set of G if X is a dominating set of G and if, for each vertex u not in X, there is a neighbouring vertex v of u in X such that the swap set (X − {v}) ∪ {u} is again a dominating set of G. The secure domination number of G is the cardinality of a smallest secure dominating set of G. A graph G is p-stable if the largest arbitrary s...
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In this paper, we study both concepts of geodetic dominatingand edge geodetic dominating sets and derive some tight upper bounds onthe edge geodetic and the edge geodetic domination numbers. We also obtainattainable upper bounds on the maximum number of elements in a partitionof a vertex set of a connected graph into geodetic sets, edge geodetic sets,geodetic domin...
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ژورنال
عنوان ژورنال: International Journal of Statistics and Applied Mathematics
سال: 2018
ISSN: 2456-1452,2456-1452
DOI: 10.22271/maths.2018.v3.i5a.01