The bondage number of graphs on topological surfaces and Teschner’s conjecture
نویسندگان
چکیده
منابع مشابه
Note on the bondage number of graphs on topological surfaces
The bondage number b(G) of a graph G is the smallest number of edges whose removal from G results in a graph with larger domination number. In this paper, we present new upper bounds for b(G) in terms of girth, order and Euler characteristic.
متن کاملThe bondage number of graphs on topological surfaces and Teschner's conjecture
The bondage number of a graph is the smallest number of its edges whose removal results in a graph having a larger domination number. We provide constant upper bounds for the bondage number of graphs on topological surfaces, improve upper bounds for the bondage number in terms of the maximum vertex degree and the orientable and non-orientable genera of the graph, and show tight lower bounds for...
متن کاملUpper bounds for the bondage number of graphs on topological surfaces
The bondage number b(G) of a graph G is the smallest number of edges of G whose removal results in a graph having the domination number larger than that of G. In a sense, the bondage number b(G) measures integrity and reliability of the domination number γ(G) with respect to the edge removal, which corresponds, e.g., to link failures in communication networks. We show that, for a graph G having...
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A dominating set of a graph is a subset D of its vertices such that every vertex not in D is adjacent to at least one member of D. The domination number of a graph G is the number of vertices in a smallest dominating set of G. The bondage number of a nonempty graph G is the size of a smallest set of edges whose removal from G results in a graph with domination number greater than the domination...
متن کاملOn the bondage number of planar and directed graphs
The bondage number b(G) of a nonempty graph G is defined to be the cardinality of the smallest set E of edges of G such that the graph G − E has domination number greater than that of G. In this paper we present a simplified proof that b(G) ≤ min{8,∆(G) + 2} for all planar graphs G, give examples of planar graphs with bondage number 6, and bound the bondage number of directed graphs.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2013
ISSN: 0012-365X
DOI: 10.1016/j.disc.2012.12.018