The Experts below are selected from a list of 2325 Experts worldwide ranked by ideXlab platform
Ashish Kumar Upadhyay - One of the best experts on this subject based on the ideXlab platform.
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Semi-equivelar maps on the torus and the Klein Bottle with few vertices
Mathematica Slovaca, 2017Co-Authors: Anand Kumar Tiwari, Ashish Kumar UpadhyayAbstract:AbstractSemi-equivelar maps are generalizations of maps on the surfaces of Archimedean solids to surfaces other than the 2-sphere. The well known 11 types of normal tilings of the plane suggest the possible types of semi-equivelar maps on the torus and the Klein Bottle. In this article we classify (up to isomorphism) semi-equivelar maps on the torus and the Klein Bottle with few vertices.
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semi equivelar maps on the torus and the Klein Bottle with few vertices
arXiv: Geometric Topology, 2015Co-Authors: Anand Kumar Tiwari, Ashish Kumar UpadhyayAbstract:Semi-Equivelar maps are generalizations of maps on the surfaces of Archimedean solids to surfaces other than the $2$-sphere. The well known 11 types of normal tilings of the plane suggest the possible types of semi-equivelar maps on the torus and the Klein Bottle. In this article we classify (up to isomorphism) semi-equivelar maps on the torus and the Klein Bottle with few vertices.
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On enumeration of a class of maps on Klein Bottle
arXiv: Combinatorics, 2015Co-Authors: Dipendu Maity, Ashish Kumar UpadhyayAbstract:We present enumerations of a class of maps on Klein Bottle which give rise to semi-equivelar maps. Semi-equivelar maps are generalizations of equivelar maps. There are eleven types of semi-equivelar maps on the Klein Bottle. These are of the types $\{3^{6}\}$, $\{4^{4}\}$, $\{6^{3}\}$, $\{3^{3},$ $4^{2}\}$, $\{3^{2},$ $4,$ $3,$ $4\}$, $\{3,$ $6,$ $3,$ $6\}$, $\{3^{4}, 6\}$, $\{4,$ $8^{2}\}$, $\{3, 12^{2}\}$, $\{4,$ $6,$ $12\}$, $\{3,$ $4,$ $6,$ $4\}$. In this article, we attempt to classify these maps.
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degree regular triangulations of torus and Klein Bottle
arXiv: Geometric Topology, 2004Co-Authors: Basudeb Datta, Ashish Kumar UpadhyayAbstract:A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular triangulation is degree-regular. In 1999, Lutz has classified all the weakly regular triangulations on at most 15 vertices. In 2001, Datta and Nilakantan have classified all the degree-regular triangulations of closed surfaces on at most 11 vertices. In this article, we have proved that any degree-regular triangulation of the torus is weakly regular. We have shown that there exists an $n$-vertex degree-regular triangulation of the Klein Bottle if and only if $n$ is a composite number $\geq 9$. We have constructed two distinct $n$-vertex weakly regular triangulations of the torus for each $n \geq 12$ and a $(4m + 2)$-vertex weakly regular triangulation of the Klein Bottle for each $m \geq 2$. For $12 \leq n \leq 15$, we have classified all the $n$-vertex degree-regular triangulations of the torus and the Klein Bottle. There are exactly 19 such triangulations, 12 of which are triangulations of the torus and remaining 7 are triangulations of the Klein Bottle. Among the last 7, only one is weakly regular.
Heping Zhang - One of the best experts on this subject based on the ideXlab platform.
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on the restricted matching extension of graphs on the torus and the Klein Bottle
Discrete Mathematics, 2012Co-Authors: Qiuli Li, Heping ZhangAbstract:Aldred and Plummer proved that every 6-connected even graph minimally embedded on the torus or the Klein Bottle is E ( 1 , n ) ( n ? 3 ) and E ( 0 , n ) ( n ? 5 ) R.E.L. Aldred, M.D. Plummer, Restricted matching in graphs of small genus, Discrete Math. 308 (2008) 5907-5921]. In this paper, we can remove the upper bounds on n by showing that every even 6-regular graph G embedded on the torus or the Klein Bottle has property E ( 1 , n - 1 ) and E ( 0 , n ) for arbitrary n ? | V ( G ) | 2 - 1 .
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dimer statistics of honeycomb lattices on Klein Bottle mobius strip and cylinder
Physica A-statistical Mechanics and Its Applications, 2012Co-Authors: Wei Li, Heping ZhangAbstract:Dimer statistics is a central problem in statistical physics. In this paper the enumerations of close-packed dimers of honeycomb lattices on Klein Bottle, Mobius strip and cylinder are considered. By establishing a Pfaffian orientation or a crossing orientation, and then computing the determinants of the skew-symmetric matrices of the resulting orientation graphs, we obtain explicit expressions of the number of close-packed dimers of the Klein-Bottle polyhex, the Mobius polyhex and the cylindrical polyhex.
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2 extendability and k resonance of non bipartite Klein Bottle polyhexes
Discrete Applied Mathematics, 2011Co-Authors: Qiuli Li, Heping ZhangAbstract:C. Thomassen classified Klein-Bottle polyhexes into five classes [C. Thomassen, Tilings of the torus and the Klein Bottle and vertex-transitive graphs on a fixed surface, Trans. Amer. Math. Soc. 323 (1991) 605-635]. In this paper, by implementing cutting and gluing operations, we reclassify the five classes of Klein-Bottle polyhexes into two classes-the bipartite case K(p,q,t) and the non-bipartite case N(p,q,t). Further, we completely characterize 2-extendable and k-resonant non-bipartite Klein-Bottle polyhexes, respectively.
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2 extendability of toroidal polyhexes and Klein Bottle polyhexes
Discrete Applied Mathematics, 2009Co-Authors: Dong Ye, Heping ZhangAbstract:A toroidal polyhex (resp. Klein-Bottle polyhex) described by a string (p,q,t) arises from a pxq-parallelogram of a hexagonal lattice by a usual torus (resp. Klein Bottle) boundary identification with a torsion t. A connected graph G admitting a perfect matching is k-extendable if |V(G)|>=2k+2 and any k independent edges can be extended to a perfect matching of G. In this paper, we characterize 2-extendable toroidal polyhexes and 2-extendable Klein-Bottle polyhexes.
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a complete characterization for k resonant Klein Bottle polyhexes
Journal of Mathematical Chemistry, 2008Co-Authors: Wai Chee Shiu, Heping ZhangAbstract:A hexagonal tessellation K(p, q, t) on Klein Bottle, a non-orientable surface with cross-cap number 2, is a finite-sized elemental benzenoid which can be produced from a p × q-parallelogram of hexagonal lattice with usual identifications of sides and with torsion t. Unlike torus, Klein Bottle polyhex K(p, q, t) is not transitive except for some degenerated cases. We shall show, however, that K(p, q, t) does not depend on t. Accordingly, criteria for K(p, q, t) to be k-resonant for every positive integer k will be given. Moreover, we shall show that K(3, q, t) of 3-resonance are fully-benzenoid.
Anand Kumar Tiwari - One of the best experts on this subject based on the ideXlab platform.
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Doubly Semiequivelar Maps on Torus and Klein Bottle
Journal of Mathematics, 2020Co-Authors: Anand Kumar Tiwari, Amit Tripathi, Yogendra Singh, Punam GuptaAbstract:A tiling of the Euclidean plane, by regular polygons, is called 2-uniform tiling if it has two orbits of vertices under the action of its symmetry group. There are 20 distinct 2-uniform tilings of the plane. Plane being the universal cover of torus and Klein Bottle, it is natural to ask about the exploration of maps on these two surfaces corresponding to the 2-uniform tilings. We call such maps as doubly semiequivelar maps. In the present study, we compute and classify (up to isomorphism) doubly semiequivelar maps on torus and Klein Bottle. This classification of semiequivelar maps is useful in classifying a category of symmetrical maps which have two orbits of vertices, named as 2-uniform maps.
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Semi-equivelar maps on the torus and the Klein Bottle with few vertices
Mathematica Slovaca, 2017Co-Authors: Anand Kumar Tiwari, Ashish Kumar UpadhyayAbstract:AbstractSemi-equivelar maps are generalizations of maps on the surfaces of Archimedean solids to surfaces other than the 2-sphere. The well known 11 types of normal tilings of the plane suggest the possible types of semi-equivelar maps on the torus and the Klein Bottle. In this article we classify (up to isomorphism) semi-equivelar maps on the torus and the Klein Bottle with few vertices.
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semi equivelar maps on the torus and the Klein Bottle with few vertices
arXiv: Geometric Topology, 2015Co-Authors: Anand Kumar Tiwari, Ashish Kumar UpadhyayAbstract:Semi-Equivelar maps are generalizations of maps on the surfaces of Archimedean solids to surfaces other than the $2$-sphere. The well known 11 types of normal tilings of the plane suggest the possible types of semi-equivelar maps on the torus and the Klein Bottle. In this article we classify (up to isomorphism) semi-equivelar maps on the torus and the Klein Bottle with few vertices.
Ed Dawson - One of the best experts on this subject based on the ideXlab platform.
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Klein Bottle routing an alternative to onion routing and mix network
International Conference on Information Security and Cryptology, 2006Co-Authors: Kun Peng, Juan Manuel Nieto, Yvo Desmedt, Ed DawsonAbstract:Traditionally, there are two methods to implement anonymous channels: free-route networks like onion routing and cascade networks like mix network. Each of them has its merits and is suitable for some certain applications of anonymous communication. Both of them have their own drawbacks, so neither of them can satisfy some applications. A third solution to anonymous channels, Klein Bottle routing, is proposed in this paper. It fills the gap between onion routing and mix network and can be widely employed in anonymous communication.
Atsuhiro Nakamoto - One of the best experts on this subject based on the ideXlab platform.
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Generating Even Triangulations on the Klein Bottle
Graphs and Combinatorics, 2018Co-Authors: Yoshihiro Asayama, Atsuhiro Nakamoto, Naoki Matsumoto, Shota OganoAbstract:We define two reductions a 4-contradiction and a 2-removal for even triangulation on a surface. It is well known that these reductions preserve some properties of graphs. The complete lists of minimal even triangulations for the sphere, the projective plane and the torus with respect to these reductions have been already determined. In this paper, we make the complete list of minimal even triangulations of the Klein Bottle and prove some applications by checking the list.
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coloring eulerian triangulations of the Klein Bottle
Graphs and Combinatorics, 2012Co-Authors: Daniel Kral, Atsuhiro Nakamoto, Bojan Mohar, Ondřej Pangrac, Yusuke SuzukiAbstract:We show that an Eulerian triangulation of the Klein Bottle has chromatic number equal to six if and only if it contains a complete graph of order six, and it is 5-colorable, otherwise. As a consequence of our proof, we derive that every Eulerian triangulation of the Klein Bottle with face-width at least four is 5-colorable.
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chromatic numbers of 6 regular graphs on the Klein Bottle
The Australasian Journal of Combinatorics, 2009Co-Authors: Atsuhiro Nakamoto, Norihito SasanumaAbstract:In this paper, we determine chromatic numbers of all 6-regular loopless graphs on the Klein Bottle. As a consequence, it follows that every simple 6-regular graph on the Klein Bottle is 5-colorable.
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k_6 minors in triangulations on the Klein Bottle
SIAM Journal on Discrete Mathematics, 2008Co-Authors: Kenichi Kawarabayashi, Raiji Mukae, Atsuhiro NakamotoAbstract:In this paper, we shall characterize triangulations on the Klein Bottle without $K_6$-minors. Our characterization implies that every $5$-connected triangulation on the Klein Bottle has a $K_6$-minor. The connectivity “5" is best possible in a sense that there is a 4-connected triangulation on the Klein Bottle without $K_6$-minors.
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5 chromatic even triangulations on the Klein Bottle
Discrete Mathematics, 2005Co-Authors: Atsuhiro NakamotoAbstract:It is known that for any closed surface F^2, every embedding on F^2 with sufficiently large representativity is 5-colorable. In this paper, we shall characterize the 5-chromatic even triangulations on the Klein Bottle with high representativity.
