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On the connectivity of Cartesian product of graphs∗
, 2013
"... We give a new alternative proof of Liouville’s formula which states that for any graphs G and H on at least two vertices, κ(G2H) = min {κ(G)H, Gκ(H), δ(G) + δ(H)}, where κ and δ denote the connectivity number and minimum degree of a given graph, respectively. The main idea of our proof is based ..."
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We give a new alternative proof of Liouville’s formula which states that for any graphs G and H on at least two vertices, κ(G2H) = min {κ(G)H, Gκ(H), δ(G) + δ(H)}, where κ and δ denote the connectivity number and minimum degree of a given graph, respectively. The main idea of our proof
Connectivity of Cartesian products of graphs
 APPL. MATH. LETT
"... A short proof for the closed expression of the edgeconnectivity of Cartesian product graphs is given and the structure of minimum edge cuts is described. It is also proved that the connectivity and edgeconnectivity of an arbitrary Cartesian power equals its minimum degree. ..."
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A short proof for the closed expression of the edgeconnectivity of Cartesian product graphs is given and the structure of minimum edge cuts is described. It is also proved that the connectivity and edgeconnectivity of an arbitrary Cartesian power equals its minimum degree.
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
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
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 498 (68 self)
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the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being kcolorable or having a aeclique (clique of density ae
Interprocedural Slicing Using Dependence Graphs
 ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS
, 1990
"... ... This paper concerns the problem of interprocedural slicinggenerating a slice of an entire program, where the slice crosses the boundaries of procedure calls. To solve this problem, we introduce a new kind of graph to represent programs, called a system dependence graph, which extends previou ..."
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Cited by 822 (85 self)
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... This paper concerns the problem of interprocedural slicinggenerating a slice of an entire program, where the slice crosses the boundaries of procedure calls. To solve this problem, we introduce a new kind of graph to represent programs, called a system dependence graph, which extends
A Spatial Logic based on Regions and Connection
 PROCEEDINGS 3RD INTERNATIONAL CONFERENCE ON KNOWLEDGE REPRESENTATION AND REASONING
, 1992
"... We describe an interval logic for reasoning about space. The logic simplifies an earlier theory developed by Randell and Cohn, and that of Clarke upon which the former was based. The theory supports a simpler ontology, has fewer defined functions and relations, yet does not suffer in terms of its us ..."
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Cited by 736 (32 self)
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We describe an interval logic for reasoning about space. The logic simplifies an earlier theory developed by Randell and Cohn, and that of Clarke upon which the former was based. The theory supports a simpler ontology, has fewer defined functions and relations, yet does not suffer in terms of its useful expressiveness. An axiomatisation of the new theory and a comparison with the two original theories is given.
A fast and high quality multilevel scheme for partitioning irregular graphs
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 1998
"... Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. ..."
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Cited by 1173 (16 self)
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Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc.
Toward a model of text comprehension and production
 Psychological Review
, 1978
"... The semantic structure of texts can be described both at the local microlevel and at a more global macrolevel. A model for text comprehension based on this notion accounts for the formation of a coherent semantic text base in terms of a cyclical process constrained by limitations of working memory. ..."
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Cited by 540 (12 self)
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are predictable only when the control schema can be made explicit. On the production side, the model is concerned with the generation of recall and summarization protocols. This process is partly reproductive and partly constructive, involving the inverse operation of the macrooperators. The model is applied
Results 1  10
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