Results 1  10
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3,908,797
A Critical Point For Random Graphs With A Given Degree Sequence
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
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Cited by 511 (8 self)
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Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0
The Minimal Number of Subtrees with a Given Degree Sequence
, 2015
"... In this paper, we investigate the structures of extremal trees which have the minimal number of subtrees in the set of all trees with a given degree sequence. In particular, the extremal trees must be caterpillar and but in general not unique. Moreover, all extremal trees with a given degree sequenc ..."
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Cited by 2 (0 self)
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In this paper, we investigate the structures of extremal trees which have the minimal number of subtrees in the set of all trees with a given degree sequence. In particular, the extremal trees must be caterpillar and but in general not unique. Moreover, all extremal trees with a given degree
Graphs with Given Degree Sequence and Maximal Spectral Radius
"... We describe the structure of those graphs that have largest spectral radius in the class of all connected graphs with a given degree sequence. We show that in such a graph the degree sequence is nonincreasing with respect to an ordering of the vertices induced by breadthfirst search. For trees the ..."
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Cited by 12 (3 self)
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We describe the structure of those graphs that have largest spectral radius in the class of all connected graphs with a given degree sequence. We show that in such a graph the degree sequence is nonincreasing with respect to an ordering of the vertices induced by breadthfirst search. For trees
The Maximum Wiener Index of Trees with Given Degree Sequences
, 2009
"... The Wiener index of a connected graph is the sum of topological distances between all pairs of vertices. Since Wang in [23] gave a mistake result on the maximum Wiener index for given tree degree sequence, in this paper, we investigate the maximum Wiener index of trees with given degree sequences an ..."
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Cited by 13 (4 self)
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The Wiener index of a connected graph is the sum of topological distances between all pairs of vertices. Since Wang in [23] gave a mistake result on the maximum Wiener index for given tree degree sequence, in this paper, we investigate the maximum Wiener index of trees with given degree sequences
Percolation on sparse random graphs with given degree sequence
, 2007
"... We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards we focus on site percolation where the vertices are retaine ..."
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Cited by 11 (0 self)
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We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards we focus on site percolation where the vertices
Ranking and unranking trees with given degree sequences
"... In this paper, we provide algorithms to rank and unrank certain degreerestricted classes of Cayley trees. Specifically, we consider classes of trees that have a given degree sequence or a given multiset of degrees. Using special properties of a bijection due to Eğecioğlu and Remmel [3], we show t ..."
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In this paper, we provide algorithms to rank and unrank certain degreerestricted classes of Cayley trees. Specifically, we consider classes of trees that have a given degree sequence or a given multiset of degrees. Using special properties of a bijection due to Eğecioğlu and Remmel [3], we show
Constructing and sampling directed graphs with given degree sequences
 New J. Phys
"... Abstract. The interactions between the components of complex networks are often directed. Proper modeling of such systems frequently requires the construction of ensembles of digraphs with a given sequence of in and outdegrees. As the number of simple labeled graphs with a given degree sequence is ..."
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Cited by 5 (1 self)
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Abstract. The interactions between the components of complex networks are often directed. Proper modeling of such systems frequently requires the construction of ensembles of digraphs with a given sequence of in and outdegrees. As the number of simple labeled graphs with a given degree sequence
The Size Of The Giant Component Of A Random Graph With A Given Degree Sequence
 COMBIN. PROBAB. COMPUT
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider a random graph having approximately i n vertices of degree i. In [12] the authors essentially show that if P i(i \Gamma 2) i ? 0 then the graph a.s. has a giant component, while if P i(i \Gamma 2) i ! 0 ..."
Abstract

Cited by 199 (0 self)
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Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider a random graph having approximately i n vertices of degree i. In [12] the authors essentially show that if P i(i \Gamma 2) i ? 0 then the graph a.s. has a giant component, while if P i(i \Gamma 2) i ! 0
Results 1  10
of
3,908,797