Bondage Number of 1-Planar Graph
نویسندگان
چکیده
منابع مشابه
Bondage and Non-bondage Number of a Fuzzy Graph
In this paper, bondage and non-bondage set of a fuzzy graph are discussed. The bondage number b(G) and non-bondage number bn(G) of a fuzzy graph G are defined. The upper bound for both b(G) and bn(G) are given. Also some results on b(G) and bn(G) are discussed. The exact values of b(G) and bn(G) are determined for several classes of fuzzy graphs. AMS Subject Classification: 03E72, 05C40, 05C72
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The bondage number b(G) of a non empty graph G is the minimum number of edger whose removal from G results in a graph having domination number greater than the domination number of G. In this paper we characterize graphs for which b(G) = p − 1 and b(G) = (γ − 1)+̇1. We also introduce the concept of uniform bondage number bu(G) and determine the exact value of bu(G) for several classes of graphs....
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A set D of a vertices in a graph G = (V,E) is said to be a total dominating set of G if every vertex in V is adjacent to some vertex in D. The total domination number γt(G) is the minimum cardinality of a total dominating set. If γt(G) = |V (G)| , the minimum cardinality of a set E0 ⊆ E(G), such that G−E0 contains no isolated vertices and γt(G− E0) > γt(G), is called the total bondage number of...
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: Applied Mathematics
سال: 2010
ISSN: 2152-7385,2152-7393
DOI: 10.4236/am.2010.12013