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ON THE ISOMORPHISM CLASSES OF TRANSVERSALS
, 2006
"... Abstract: In this paper, we prove that there does not exist a subgroup H of a finite group G such that the number of isomorphism classes of right transversals of H in G is two. Key words: Transversals; Right quasigroup; Minimal counter example. 2000 Mathematical Subject classification: 20D60, 20N05. ..."
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Abstract: In this paper, we prove that there does not exist a subgroup H of a finite group G such that the number of isomorphism classes of right transversals of H in G is two. Key words: Transversals; Right quasigroup; Minimal counter example. 2000 Mathematical Subject classification: 20D60, 20N05
On 2switches and isomorphism classes
 Discrete Math
"... A 2switch is an edge addition/deletion operation that changes adjacencies in the graph while preserving the degree of each vertex. A well known result states that graphs with the same degree sequence may be changed into each other via sequences of 2switches. We show that if a 2switch changes the ..."
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Cited by 3 (3 self)
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the isomorphism class of a graph, then it must take place in one of four configurations. We also present a sufficient condition for a 2switch to change the isomorphism class of a graph. As consequences, we give a new characterization of matrogenic graphs and determine the largest hereditary graph family whose
Isomorphism classes of certain complete intersections
 In preparation
, 2008
"... A longstanding problem in Commutative Algebra is the classification of Artin algebras. We know that there exists a finite number of isomorphism classes of Artin ..."
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Cited by 3 (2 self)
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A longstanding problem in Commutative Algebra is the classification of Artin algebras. We know that there exists a finite number of isomorphism classes of Artin
Isomorphism classes of Ahypergeometric systems
 Compositio Math
, 2001
"... For a finite set A of integral vectors, Gel’fand, Kapranov and Zelevinskii defined a system of differential equations with a parameter vector as a Dmodule, which system is called an Ahypergeometric (or a GKZ hypergeometric) system. Classifying the parameters according to the Disomorphism classes ..."
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Cited by 17 (4 self)
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For a finite set A of integral vectors, Gel’fand, Kapranov and Zelevinskii defined a system of differential equations with a parameter vector as a Dmodule, which system is called an Ahypergeometric (or a GKZ hypergeometric) system. Classifying the parameters according to the Disomorphism classes
On Distances between Isomorphism Classes of Graphs
"... In 1986, Chartrand, Saba and Zou [3] defined a measure of the distance between (the isomorphism classes of) two graphs based on ‘edge rotations’. Here, that measure and two related measures are explored. Various bounds, exact values for classes of graphs and relationships are proved, and the three m ..."
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In 1986, Chartrand, Saba and Zou [3] defined a measure of the distance between (the isomorphism classes of) two graphs based on ‘edge rotations’. Here, that measure and two related measures are explored. Various bounds, exact values for classes of graphs and relationships are proved, and the three
EDGEDISTANCE BETWEEN ISOMORPHISM CLASSES OF GRAPHS
, 1984
"... here edgedistance) between isomorphism classes of graphs, based on the maximum number of edges of common subgraph. This paper concerns the graph whose vertex set is the set of all isomorphism classes of graphs with n vertices and in which two vertices are adjacent if and only if their edgedistance ..."
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here edgedistance) between isomorphism classes of graphs, based on the maximum number of edges of common subgraph. This paper concerns the graph whose vertex set is the set of all isomorphism classes of graphs with n vertices and in which two vertices are adjacent if and only if their edge
On Isomorphism Classes of Generalized Fibonacci Cubes
, 2014
"... The generalized Fibonacci cube Qd(f) is the subgraph of the dcube Qd induced on the set of all strings of length d that do not contain f as a substring. It is proved that if Qd(f) ∼ = Qd(f ′) then f = f′. The key tool to prove this result is a result of Guibas and Odlyzko about the autocorrela ..."
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The generalized Fibonacci cube Qd(f) is the subgraph of the dcube Qd induced on the set of all strings of length d that do not contain f as a substring. It is proved that if Qd(f) ∼ = Qd(f ′) then f = f′. The key tool to prove this result is a result of Guibas and Odlyzko about the autocorrelation polynomial associated to a binary string. It is also proved that there exist pairs of strings f, f ′ such that Qd(f) ∼ = Qd(f ′), where f ≥ 23 (d + 1) and f ′ cannot be obtained from f by its reversal or binary complementation. Strings f and f ′ with f = f′ = d − 1 for which Qd(f) ∼ = Qd(f′) are characterized.
Isomorphism classes of Edwards curves over finite fields
"... Edwards curves are an alternate model for elliptic curves, which have attracted notice in cryptography. We give exact formulas for the number of Fqisomorphism classes of Edwards curves and twisted Edwards curves. This answers a question recently asked by R. Farashahi and I. Shparlinski. 1 1 ..."
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Edwards curves are an alternate model for elliptic curves, which have attracted notice in cryptography. We give exact formulas for the number of Fqisomorphism classes of Edwards curves and twisted Edwards curves. This answers a question recently asked by R. Farashahi and I. Shparlinski. 1 1
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