1. Chepoi Victor, Dragan Feodor F., Vaxes Yann: Distance and routing labeling schemes for non-positively curved plane graphs. J. Algorithms 61 (2006), no. 2, 60-88.Boštjan Brešar, 2006, review, book review, critique Keywords: mathematics, graph theory, distance labeling scheme, routing labeling scheme, efficient algorithms Published: 31.05.2012; Views: 1115; Downloads: 17 Link to full text |
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3. Different Higgs models and the number of Higgs particlesLeila Marek-Crnjac, 2006, original scientific article Abstract: In this short paper we discuss some interesting Higgs models. It is concluded that the most likely scheme for the Higgs particles consists of five physical Higgs particles. These are two charged H▫$^+$▫, H▫$^-$▫ and three neutrals ▫$h^0$▫, H▫$^0$▫, A▫$^0$▫. Further more the most probably total number of elementary particles for each model is calculated [El Naschie MS. Experimental and theoretical arguments for the number of the mass of the Higgs particles. Chaos, Solitons & Fractals 2005;23:1091-8; El Naschie MS. Determining the mass of the Higgs and the electroweak bosons. Chaos, Solitons & Fractals 2005;24:899-905; El Naschie MS.On 366 kissing spheres in 10 dimensions, 528 P-Brane states in 11 dimensions and the 60 elementary particles of the standard model. Chaos, Solitons & Fractals 2005;24:447-57]. Keywords: mathematics, Higgs models, Higgs particles, Riemann tensor, Killing vector, minimal super symmetric standard model Published: 30.05.2012; Views: 1776; Downloads: 55 Link to full text |
4. On Euclidean algebra of hermitian operators on a quadratic Hilbert spaceRok Strašek, 2006, original scientific article Abstract: We solve the problem of finding the best possible constant of ultraprimeness for the special class of Euclidean algebra called algebra of hermitian operators on a quaternionic Hilbert space. More precisely, we prove that for algebra of hermitian operators, equipped with spectral norm, the best possibleconstant of ultraprimeness is 1/2. Keywords: mathematics, Euclidean algebras, quaternionic Hilbert space, ultraprime algebras, Jacobson-McCrimmon operator, spectral norm Published: 30.05.2012; Views: 1104; Downloads: 29 Link to full text |
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8. On edge connectivity of direct products of graphsXiang-Lan Cao, Špela Brglez, Simon Špacapan, Elkin Vumar, 2011, original scientific article Abstract: Let ▫$lambda(G)$▫ be the edge connectivity of ▫$G$▫. The direct product of graphs ▫$G$▫ and ▫$H$▫ is the graph with vertex set ▫$V(G times H) = V(G) times V(H)$▫, where two vertices ▫$(u_1,v_1)$▫ and ▫$(u_2,v_2)$▫ are adjacent in ▫$G times H$▫ if ▫$u_1u_2 in E(G)$▫ and ▫$v_1v_2 in E(H)$▫. We prove that ▫$lambda(G times K_n) = min{n(n-1)lambda(G), (n-1)delta(G)}$▫ for every nontrivial graph ▫$G$▫ and ▫$n geqslant 3$▫. We also prove that for almost every pair of graphs ▫$G$▫ and ▫$H$▫ with ▫$n$▫ vertices and edge probability ▫$p$▫, ▫$G times H$▫ is ▫$k$▫-connected, where ▫$k=O((n/log n)^2)$▫. Keywords: mathematics, graph theory, combinatorial problems, connectivity, direct product, graph product, separating set Published: 01.06.2012; Views: 1615; Downloads: 189 Link to full text |
9. 2-local 3/4-competitive algorithm for multicoloring hexagonal graphsPetra Šparl, Janez Žerovnik, 2005, original scientific article Abstract: An important optimization problem in the design of cellular networks is to assign sets of frequencies to transmitters to avoid unacceptable interference.A cellular network is generally modeled as a subgraph of the infinite triangular lattice. Frequency assignment problem can be abstracted asa multicoloring problem on a weighted hexagonal graph, where the weights represent the number of calls to be assigned at vertices. In this paper we present a distributed algorithm for multicoloring hexagonal graphs using only the local clique numbers ▫$omega_1(v)$▫ and ▫$omega_2(v)$▫ at each vertex v of the given hexagonal graph, which can be computed from local information available at thevertex. We prove the algorithm uses no more than ▫$4omega(G)/3$▫ colors for any hexagonal graph G, without explicitly computing the global clique number ▫$omega(G)$▫. We also prove that our algorithm is 2-local, i.e., the computation at a vertex v ▫$in$▫ G uses only information about the demands of vertices whose graph distance from v is less than or equal to 2. Keywords: mathematics, graph theory, graph colouring, 2-local distributed algorithm, cellular networks, frequency planning Published: 01.06.2012; Views: 1435; Downloads: 69 Link to full text |
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