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Abstract
A 2-dominating set of a graph G=(V,E) is a set D of vertices of G such that every vertex of V(G)D has at least two neighbors in D. The 2-domination number of a graph G, denoted by gamma_2(G), is the minimum cardinality of a 2-dominating set of G. The 2-bondage number of G, denoted by b_2(G), is the minimum cardinality among all sets of edges E' subseteq E such that gamma_2(G-E') > gamma_2(G). If for every E' subseteq E we have gamma_2(G-E') = gamma_2(G), then we define b_2(G) = 0, and we say that G is a gamma_2-strongly stable graph. First we discuss the basic properties of 2-bondage in graphs. We find the 2-bondage numbers for several classes of graphs. Next we show that for every non-negative integer there exists a tree with such 2-bondage number. Finally, we characterize all trees with 2-bondage number equaling one or two.
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
no. 90,
pages 1358 - 1365,
ISSN: 0020-7160 - Language:
- English
- Publication year:
- 2013
- Bibliographic description:
- Krzywkowski M.: 2-bondage in graphs// INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS. -Vol. 90, nr. 7 (2013), s.1358-1365
- DOI:
- Digital Object Identifier (open in new tab) 10.1080/00207160.2012.752817
- Verified by:
- Gdańsk University of Technology
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