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233,154
On the Graphs of HoffmanSingleton and HigmanSims
"... We propose a new elementary definition of the HigmanSims graph in which the 100 vertices are parametrised with Z 4 5 and adjacencies are described by linear and quadratic equations. This definition extends Robertson's pentagonpentagram definition of the Ho#manSingleton graph and is obta ..."
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Cited by 5 (0 self)
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and is obtained by studying maximum cocliques of the Ho#manSingleton graph in Robertson's parametrisation. The new description is used to count the 704 Ho#manSingleton subgraphs in the HigmanSims graph, and to describe the two orbits of the simple group HS on them, including a description of the doubly
The HoffmanSingleton Graph and Its Automorphisms
 J. Algebraic Combin
, 2003
"... We describe the HomanSingleton graph geometrically, showing that it is closely related to the incidence graph of the ane plane over Z5 . This allows us to construct all automorphisms of the graph. ..."
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Cited by 7 (1 self)
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We describe the HomanSingleton graph geometrically, showing that it is closely related to the incidence graph of the ane plane over Z5 . This allows us to construct all automorphisms of the graph.
The Hoffman–Singleton graph and outer automorphisms
, 2005
"... In this note, I show that the Hoffman–Singleton graph can be constructed from a nontrivial outer automorphism of S6 and vice versa. I have learned from Peter Cameron that this was already known by Higman. A graph (G, E) is a binary, symmetric, and antireflexive relation E on the set G. A Moore gra ..."
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In this note, I show that the Hoffman–Singleton graph can be constructed from a nontrivial outer automorphism of S6 and vice versa. I have learned from Peter Cameron that this was already known by Higman. A graph (G, E) is a binary, symmetric, and antireflexive relation E on the set G. A Moore
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
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.
GromovWitten classes, quantum cohomology, and enumerative geometry
 Commun. Math. Phys
, 1994
"... The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological ..."
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Cited by 484 (3 self)
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The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological
Probabilistic Roadmaps for Path Planning in HighDimensional Configuration Spaces
 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 1996
"... A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collisionfree configurations and whose edg ..."
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Cited by 1276 (124 self)
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A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collisionfree configurations and whose
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
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Cited by 543 (11 self)
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of graphs in twodimensional manifolds. This structure represents simultaneously an embedding, its dual, and its mirror image. Furthermore, just two operators are sufficient for building and modifying arbitrary diagrams.
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