Results 1 - 10 of 997

GROUP MAGIC LABELING OF CYCLES WITH A COMMON VERTEX

by unknown authors
"... Let G = (V, E) be a connected simple graph. For any non-trivial additive abelian group A, let A * = A − {0}. A function f: E (G) → A * is called a labeling of G. Any such labeling induces a map f +: V (G) → A, defined by f+(v) = ∑ f(uv), where the sum is over all uv E(G). If there exist a lab ..."
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labeling f whose induced map on V (G) is a constant map, we say that f is an A-magic labeling of G and that G is an A-magic graph. In this paper we obtained the group magic labeling of two or more cycles with a common vertex.

WHEN DO THREE LONGEST PATHS HAVE A COMMON VERTEX?

by Maria Axenovich
"... It is well known that any two longest paths in a connected graph share a vertex. It is also known that there are connected graphs where 7 longest paths do not share a common vertex. It was conjectured that any three longest paths in a connected graph have a vertex in common. In this note we prove t ..."
Abstract - Cited by 3 (0 self) - Add to MetaCart
It is well known that any two longest paths in a connected graph share a vertex. It is also known that there are connected graphs where 7 longest paths do not share a common vertex. It was conjectured that any three longest paths in a connected graph have a vertex in common. In this note we prove

Measurement of the Non-Common Vertex Error of a Double Corner Cube

by Alireza Azizi , Martin Marcin , Douglas Moore , Steve Moser , John Negron , Eung-Gi Paek , Daniel Ryan , Alex Abramovici , Paul Best , Ian Crossfield , Bijan Nemati , Tim Neville , B Platt , Leonard Wayne
"... ABSTRACT The Space Interferometry Mission (SIM) requires the control of the optical path of each interferometer with picometer accuracy. Laser metrology gauges are used to measure the path lengths to the fiiducial corner cubes at the siderostats. Due to the geometry of SIM a single corner cube does ..."
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-commonalty of the vertices and correct for the error in orbit. SIM requires that the non-common vertex error (NCVE) of the double corner cube to be less than 6 µm. The required accuracy for the knowledge of the NCVE is less than 1 µm. This paper explains a method of measuring non-common vertices of a brassboard double

Algebraic Graph Theory

by Chris Godsil, Mike Newman , 2011
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
Abstract - Cited by 892 (13 self) - Add to MetaCart
is the investigation of the relation between properties of a graph and the spectrum of its adjacency matrix. A central topic and important source of tools is the theory of association schemes. An association scheme is, roughly speaking, a collection of graphs on a common vertex set which fit together in a highly

A Data Structure for Dynamic Trees

by Daniel D. Sleator, Robert Endre Tarjan , 1983
"... A data structure is proposed to maintain a collection of vertex-disjoint trees under a sequence of two kinds of operations: a link operation that combines two trees into one by adding an edge, and a cut operation that divides one tree into two by deleting an edge. Each operation requires O(log n) ti ..."
Abstract - Cited by 347 (21 self) - Add to MetaCart
A data structure is proposed to maintain a collection of vertex-disjoint trees under a sequence of two kinds of operations: a link operation that combines two trees into one by adding an edge, and a cut operation that divides one tree into two by deleting an edge. Each operation requires O(log n

Smallest Limited Vertex-to-Vertex Snakes of Unit Triangles

by Heiko Harborth Diskrete, Heiko Harborth
"... A sequence T = hT 1 ; T 2 ; : : : ; T n i of regular triangles of unit side lengths is called a vertex-to-vertex snake if T i " T j is a common vertex The work was supported by Hungarian State Eotvos Fellowship and by Hungarian Scientific Research Fund No. F019449. ..."
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A sequence T = hT 1 ; T 2 ; : : : ; T n i of regular triangles of unit side lengths is called a vertex-to-vertex snake if T i " T j is a common vertex The work was supported by Hungarian State Eotvos Fellowship and by Hungarian Scientific Research Fund No. F019449.

Laplacian Surface Editing

by Olga Sorkine, Daniel Cohen-Or, Yaron Lipman, Christian Rössl, Hans-Peter Seidel, Marc Alexa , 2004
"... Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. We p ..."
Abstract - Cited by 235 (27 self) - Add to MetaCart
Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. We

Vertex Arrays

by unknown authors
"... I 3D graphics geometric models can be specified in various ways. I Polygonal modelling where objects are defined by sets of polygons, and in turn vertices, is the most common. ..."
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I 3D graphics geometric models can be specified in various ways. I Polygonal modelling where objects are defined by sets of polygons, and in turn vertices, is the most common.

Vertex operator algebras and operads

by Yi-zhi Huang, James Lepowsky , 1993
"... Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, n-ary operations for all n greater than or equal to 0, not just binary products. In this paper, a reformulation o ..."
Abstract - Cited by 29 (6 self) - Add to MetaCart
of the notion of vertex operator algebra in terms of operads is presented. This reformulation shows that the rich geometric structure revealed in the study of conformal field theory and the rich algebraic structure of the theory of vertex operator algebras share a precise common foundation in basic operations

Vertex-based Anisotropic Texturing

by Marc Olano, Shrijeet Mukherjee, Angus Dorbie - In Proc. of Eurographics/SIGGRAPH Graphics Hardware Workshop , 2001
"... MIP mapping is a common method used by graphics hardware to avoid texture aliasing. In many situations, MIP mapping over-blurs in one direction to prevent aliasing in another. Anisotropic texturing reduces this blurring by allowing differing degrees of filtering in different directions, but is not a ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
MIP mapping is a common method used by graphics hardware to avoid texture aliasing. In many situations, MIP mapping over-blurs in one direction to prevent aliasing in another. Anisotropic texturing reduces this blurring by allowing differing degrees of filtering in different directions
Results 1 - 10 of 997