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Two new optimal ternary two-weight codes and strongly regular graphs

T.Aaron Gulliver
1996 Discrete Mathematics  
Based upon the code parameters, the existence of two strongly regular graphs is established.  ...  It is well known that two-weight codes result in strongly regular graphs if the code is projective.  ...  Andries Brouwer for bringing this connection between codes and graphs to his attention.  ... 
doi:10.1016/0012-365x(94)00264-j fatcat:zjmgx6i54vee3alfscsto7kcza

A new two-weight code and strongly regular graph

T.A. Gulliver
1996 Applied Mathematics Letters  
It is well known that two-weight codes result in strongly regular graphs if the code is projective. In this paper a (154,6,99) quasi-cyclic two-weight code over OF (3) is presented.  ...  Let C be a linear (n, k, d) code over GF(q).  ...  Many QC codes were found with dmin --99, but one was found with only one other nonzero weight. This search took less than 1 minute on a SUN SPARCstation 2 computer.  ... 
doi:10.1016/0893-9659(96)00004-3 fatcat:ufmzjsdsdzhazcpcffpaan5esq

Page 798 of Mathematical Reviews Vol. , Issue 90B [page]

1990 Mathematical Reviews  
The authors give both constructions and nonexistence results and provide a table listing all feasible parameter sets for primitive strongly regular graphs with a strongly regular decomposition and < 300  ...  G. (1-MI) Strongly regular graphs with strongly regular decomposition. Linear Algebra Appl. 114(115) (1989), 379-398.  ... 

HOW TO SELECT PAIRED COMPARISONS IN AHP OF INCOMPLETE INFORMATION-STRONGLY REGULAR GRAPH DESIGN

Keyi Wang, Iwaro Takahashi
1998 Journal of the Operations Research Society of Japan  
Since SR graphs are rather diMcult to be constructed, we generalize them to quasi-strongly regular (quasi-SR) graphs, and propose quasi-SR design based on quasi-SR graphs.  ...  The problem is how to select pairs to be compared in S., that is, a design to get data, We propose the strongly regular (SR) design based on strongly regular graphs, and by numerical simulatiDn show that  ...  More precisely, for given n, what is the best subset of size m to be selected in S., to estimate We propose the strongly regular (SR) design based on strongly regular graphs, and by numerical simulation  ... 
doi:10.15807/jorsj.41.311 fatcat:f5wnegalifchra4nrvei3abndq

Quasi-residual designs, 112-designs, and strongly regular multigraphs

Klaus Metsch
1995 Discrete Mathematics  
Suppose that the parameters (m, n, u, y, R) of a strongly regular multigraph can be written in the form m = k, n=r-i, u=k2A, y=k(k-l)(A-l), R=k(r-1) for some integers k 2 3, r and 1.  ...  Suppose that r is a strongly regular multigraph whose parameters (m, n, u, y, R) can be written in the form m = r, n = k + r + c -1t, p = rt, y = rc, R = r(kl), with integers r 2 3 and t 2 1, and real  ...  The collinearity graph of a l~design with parameters (r, k, t, c) is a strongly regular multigraph with parameters (m, n, p, y, R) given by (1.6) m:= r, n:=k+r+c-l-t, u=rt, y:=rc, R:=r(k-1).  ... 
doi:10.1016/0012-365x(94)00014-a fatcat:ai7b6skkw5hl3jnx7vvhj53sqm

Steiner triple systems and strongly regular graphs

I.Š.o. Aliev, Esther Seiden
1969 Journal of Combinatorial Theory  
The Steiner triple systems are characterized in terms of strongly regular graphs provided that the number of cliques exceed 67.  ...  A. A. Zykov for inviting the second author to Novosibirsk and thus providing the facilities for our joint work, which we do hope to continue.  ...  Bose and Laskar [3] considered graphs G with the following properties: (C1) G is connected and regular of valence r(k --1). (C2) G is edge regular with edge degree (k --2) q-a.  ... 
doi:10.1016/s0021-9800(69)80102-x fatcat:ckkdqjyko5br3l772pkb57vg2i

Hereditarily extended properties, quasi-random graphs and not necessarily induced subgraphs

Mikl�s Simonovits, Vera T. S�s
1997 Combinatorica  
Here the properties are strongly connected to counting not necessarily induced subgraphs of a given type, while in a subsequent paper we shall investigate the properties connected with counting induced  ...  Dedicated to the memory of Paul Erdbs Recently nmch attention has been focused on the theory of quasi-random graph and hypergraph properties.  ...  U V (n) be a Szemer6di Partition of Gn with the parameters gt = ~, ~ = t. Let X C Vi, IX[ = 89 Suppose all the pairs (vi(n),vj(n)),--l<i<j<,-1 are g-regular.  ... 
doi:10.1007/bf01195005 fatcat:riblmkxljrf4bn2tcj7ml7qoqe

Trivial pursuit: Remarks on the main gap

John T. Baldwin, Leo Harrington
1987 Annals of Pure and Applied Logic  
A dependence relation is trivial when a single point which depends on a pair of independent points depends on just one of them.  ...  Section 1 of this paper contains some technical results about trivial types.  ...  Let p, q E S(A) be stationary trivial types with p ,k! q. Suppose p is regular and for some +, (q, C#J) is strongly regular.  ... 
doi:10.1016/0168-0072(87)90001-7 fatcat:6bezaadvgrb4xfis47g3lmsu2u

Quasi-quadrics and related structures

Frank De Clerck, Nicholas A. Hamilton, Christine M. O'Keefe, Tim Penttila
2000 The Australasian Journal of Combinatorics  
When n is even, quasi-quadrics have three sizes of intersection with respect to hyperplanes. Certain of these may be used to construct antipodal distance regular covers of complete graphs.  ...  In a projective space PG(n, q) a quasi-quadric is a set of points that has the same intersection numbers with respect to hyperplanes as a nondegenerate quadric in that space.  ...  ,bd-1;C1,C2,'" ,Cd}' The graph r is strongly regular with parameters (IV\, k, ,\, /-l) if it is regular with valency k and if the number of vertices joined to two given adjacent vertices is A and the number  ... 
dblp:journals/ajc/ClerckHOP00 fatcat:rmguzexhbfej7lyas4rx3vf4wq

Cheeger isoperimetric constant of Gromov hyperbolic manifolds and graphs [article]

Álvaro Martínez-Pérez, José M. Rodríguez
2016 arXiv   pre-print
We characterize the hyperbolic manifolds and graphs (with bounded local geometry) verifying this isoperimetric inequality, in terms of their Gromov boundary.  ...  Furthermore, we characterize the trees with isoperimetric inequality (without any hypothesis).  ...  Let {G k } kN be a sequence of graphs isometric to G with v k ∈ V (G k ) for each kN.  ... 
arXiv:1605.04394v1 fatcat:6u62fn44ijgghkvaswvq3k73li

Nonlinear Quantum Search [article]

Thomas G. Wong
2015 arXiv   pre-print
Jointly optimizing these resources results in an overall scaling of N^1/4, which is a significant, but not unreasonable, improvement over the N^1/2 scaling of Grover's algo.  ...  Further, strongly reg graphs, which have no global sym, are sufficiently complete for quant search on them to asymp behave like unstruct search.  ...  graph, which is a strongly regular graph with parameters (10,3,0,1).  ... 
arXiv:1506.04388v1 fatcat:bnpwjxqidja6ziovukeaokttse

Effect of fluctuations on the NMR relaxation beyond the Abrikosov vortex state

A. Glatz, A. Galda, A. A. Varlamov
2015 Physical Review B  
The first one is its decrease in result of suppression of quasi-particle density of states (DOS) due to formation of fluctuation Cooper pairs (FCP).  ...  As a result, different scenarios with either growth or decrease of the NMR relaxation rate are possible upon approaching the normal metal - type-II superconductor transition.  ...  ACKNOWLEDGEMENTS We express our deep gratitude to A. Rigamonti and A. Lasciafari for attracting our attention to their experiments and numerous elucidating discussions.  ... 
doi:10.1103/physrevb.92.054513 fatcat:x255m4ny6fccxmsqh4hlqtfuma

Page 1310 of Mathematical Reviews Vol. , Issue 91C [page]

1991 Mathematical Reviews  
The friendship theorem says that the graph cannot be regular for A = 1. The authors would like to generalize this to the nonexistence of strongly regular graphs with constant A= and x.  ...  Stembridge (1-MI) 91c:05202 05E30 Hartnell, Bert L. (3-STMR); Jeans, Neville (3-MB); Kocay, William (3-MB) Parameter sets for a class of strongly regular graphs. J. Combin. Math. Combin.  ... 

Rigidity for Quasi-Möbius Actions on Fractal Metric Spaces [article]

Kyle Kinneberg
2016 arXiv   pre-print
Kleiner proved a rigidity theorem for expanding quasi-Möbius group actions on Ahlfors n-regular metric spaces with topological dimension n.  ...  This led naturally to a rigidity result for quasi-convex geometric actions on CAT(-1)-spaces that can be seen as a metric analog to the "entropy rigidity" theorems of U. Hamenstädt and M. Bourdon.  ...  Let Z be a compact, Ahlfors n-regular met- ric space with topological dimension n1. Suppose that Γ y Z is a uniformly quasi-Möbius group action that is cocompact on triples.  ... 
arXiv:1308.0639v2 fatcat:gtcsf422krabbazwvc5sfzsaii

Regularized and inertial algorithms for common fixed points of nonlinear operators

Paul-Emile Maingé
2008 Journal of Mathematical Analysis and Applications  
This paper deals with a general fixed point iteration for computing a point in some nonempty closed and convex solution set included in the common fixed point set of a sequence of mappings on a real Hilbert  ...  Under classical conditions on the operators and the parameters, we prove that the sequence of iterates generated by our scheme converges strongly to the element of minimal norm in the solution set.  ...  However the products T n of a quasi-nonexpansive mapping T are obviously quasi-nonexpansive, hence not necessarily continuous (for n large enough), on the contrary to the case when T is asymptotically  ... 
doi:10.1016/j.jmaa.2008.03.028 fatcat:gt5trm2wx5bmrjc7yxnswsefue
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