Bondage Numbers in Graphs
نویسندگان
چکیده
منابع مشابه
Roman bondage numbers of some graphs
A Roman dominating function on a graph G = (V,E) is a function f : V → {0, 1, 2} satisfying the condition that every vertex u with f(u) = 0 is adjacent to at least one vertex v with f(v) = 2. The weight of a Roman dominating function is the value f(G) = ∑ u∈V f(u). The Roman domination number of G is the minimum weight of a Roman dominating function on G. The Roman bondage number of a nonempty ...
متن کاملThe bondage numbers of graphs with small crossing numbers
The bondage number b(G) of a nonempty graph G is the cardinality of a smallest edge set whose removal from G results in a graph with domination number greater than the domination number (G) ofG. Kang andYuan proved b(G) 8 for every connected planar graph G. Fischermann, Rautenbach and Volkmann obtained some further results for connected planar graphs. In this paper, we generalize their results ...
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The bondage number of a graph G is the minimum number of edges whose removal results in a graph with larger domination number.A dominating setD is called an efficient dominating set ofG if |N−[v]∩D|=1 for every vertex v ∈ V (G). In this paper we establish a tight lower bound for the bondage number of a vertex-transitive graph. We also obtain upper bounds for regular graphs by investigating the ...
متن کاملOn Bondage Numbers of Graphs: A Survey with Some Comments
The domination number of a graph G is the smallest number of vertices which dominate all remaining vertices by edges of G. The bondage number of a nonempty graphG is the smallest number of edges whose removal fromG results in a graph with domination number greater than the domination number of G. The concept of the bondage number was formally introduced by Fink et al. in 1990. Since then, this ...
متن کاملNote on Conjectures of Bondage Numbers of Planar Graphs
The bondage number of a graph G is the cardinality of a smallest set of edges whose removal results in a graph with domination number larger than that of G. The bondage number measures to some extent the robustness of a network with respect to link failure. This note mainly considers some conjectures on the bondage number of a planar graph, and shows limitations of known methods and presents so...
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ژورنال
عنوان ژورنال: Shanlax International Journal of Arts, Science and Humanities
سال: 2022
ISSN: ['2321-788X']
DOI: https://doi.org/10.34293/sijash.v10is1.5263