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A characterization of locatingdomination edge critical graphs
"... A locatingdominating set D of a graph G =(V (G),E(G)) is a set D ⊆ V (G) such that every vertex of V (G) − D is adjacent to a vertex of D and for every pair of distinct vertices u, v in V (G) − D, N(u) ∩ D = N(v) ∩ D. The minimum cardinality of a locatingdominating set is denoted by γL(G). A ..."
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graph G is said to be a locating domination edge removal critical graph, orjustγ + LERcritical graph, if γL(G−e)>γL(G) for all e ∈ E(G). The purpose of this paper is to characterize the class ofERcritical graphs. γ + L 1
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
Edge Detection
, 1985
"... For both biological systems and machines, vision begins with a large and unwieldy array of measurements of the amount of light reflected from surfaces in the environment. The goal of vision is to recover physical properties of objects in the scene, such as the location of object boundaries and the s ..."
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Cited by 1277 (1 self)
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For both biological systems and machines, vision begins with a large and unwieldy array of measurements of the amount of light reflected from surfaces in the environment. The goal of vision is to recover physical properties of objects in the scene, such as the location of object boundaries
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.
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
A computational approach to edge detection
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1986
"... AbstractThis paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal ..."
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Cited by 4621 (0 self)
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AbstractThis paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal
Locatingdominating codes in cycles
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 49 (2011), PAGES 177–194
, 2011
"... The smallest cardinality of an rlocatingdominating code in a cycle Cn of length n is denoted by M LD r (Cn). In this paper, we prove that for any r ≥ 5andn ≥ nr when nr is large enough (nr = O(r3)) we have n/3 ≤ M LD r (Cn) ≤ n/3 +1 ifn ≡ 3(mod6)andMLD r (Cn) =⌈n/3⌉ otherwise. Moreover, we determ ..."
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Cited by 2 (1 self)
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The smallest cardinality of an rlocatingdominating code in a cycle Cn of length n is denoted by M LD r (Cn). In this paper, we prove that for any r ≥ 5andn ≥ nr when nr is large enough (nr = O(r3)) we have n/3 ≤ M LD r (Cn) ≤ n/3 +1 ifn ≡ 3(mod6)andMLD r (Cn) =⌈n/3⌉ otherwise. Moreover, we
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
Results 1  10
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1,081,256