On the bondage number of planar and directed graphs
نویسندگان
چکیده
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.
منابع مشابه
The Bondage Number of Graphs with Crossing Number Less than Four
The bondage number b(G) of a graph G is the smallest number of edges whose removal results in a graph with domination number greater than the domination number of G. Kang and Yuan [Bondage number of planar graphs. Discrete Math. 222 (2000), 191198] proved b(G) 6 min{8,∆+ 2} for every connected planar graph G, where ∆ is the maximum degree of G. Later Carlson and Develin [On the bondage number o...
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 306 شماره
صفحات -
تاریخ انتشار 2006