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Perfect kdomination in graphs
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 48 (2010), PAGES 175–184
, 2010
"... Let k be a positive integer. A vertex subset D of a graph G =(V,E) is a perfect kdominating set of G if every vertex v of G, not in D, is adjacent to exactly k vertices of D. The minimum cardinality of a perfect kdominating set of G is the perfect kdomination number γkp(G). In this paper, we gene ..."
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Let k be a positive integer. A vertex subset D of a graph G =(V,E) is a perfect kdominating set of G if every vertex v of G, not in D, is adjacent to exactly k vertices of D. The minimum cardinality of a perfect kdominating set of G is the perfect kdomination number γkp(G). In this paper, we
The kDominating Graph
 Graphs and Combinatorics
, 2013
"... Abstract. Given a graphG, the kdominating graph ofG, Dk(G), is defined to be the graph whose vertices correspond to the dominating sets of G that have cardinality at most k. Two vertices in Dk(G) are adjacent if and only if the corresponding dominating sets of G differ by either adding or deleting ..."
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Abstract. Given a graphG, the kdominating graph ofG, Dk(G), is defined to be the graph whose vertices correspond to the dominating sets of G that have cardinality at most k. Two vertices in Dk(G) are adjacent if and only if the corresponding dominating sets of G differ by either adding
NordhausGaddum Bounds for kDomination in Graphs
, 2007
"... A kdominating set of a graph G is a set S of vertices of G such that every vertex outside of S has k neighbors in S. The kdomination number of G, written γk(G), is the size of the smallest kdominating set in G. In this paper, we derive sharp upper and lower bounds on γk(G) + γk(G) and γk(G)γk(G), ..."
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A kdominating set of a graph G is a set S of vertices of G such that every vertex outside of S has k neighbors in S. The kdomination number of G, written γk(G), is the size of the smallest kdominating set in G. In this paper, we derive sharp upper and lower bounds on γk(G) + γk(G) and γk
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Books in graphs
, 2008
"... A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α) ..."
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Cited by 2380 (22 self)
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A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α
A Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
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Cited by 627 (44 self)
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Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized
Results 1  10
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1,854,782