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12. Minimal normal subgroups of transitive permutation groups of square-free degreeEdward Dobson, Aleksander Malnič, Dragan Marušič, Lewis A. Nowitz, 2007, izvirni znanstveni članek Opis: It is shown that a minimal normal subgroup of a transitive permutation group of square-free degree in its induced action is simple and quasiprimitive, with three exceptions related to ▫$A_5$▫, ▫$A_7$▫, and PSL(2,29). Moreover, it is shown that a minimal normal subgroup of a 2-closed permutation group of square-free degree in its induced action is simple. As an almost immediate consequence, it follows that a 2-closed transitive permutation group of square-free degree contains a semiregular element of prime order, thus giving a partial affirmative answer to the conjecture that all 2-closed transitive permutation groups contain such an element (see [D. Marušic, On vertex symmetric digraphs,Discrete Math. 36 (1981) 69-81; P.J. Cameron (Ed.), Problems from the fifteenth British combinatorial conference, Discrete Math. 167/168 (1997) 605-615]).
Ključne besede: mathematics, graph theory, transitive permutation group, 2-closed group, square-free degree, semiregular automorphism, vertex-transitive graph
Objavljeno v RUP: 03.04.2017; Ogledov: 2406; Prenosov: 89
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13. On the spectral radius of unicyclic graphs with prescribed degree sequenceFrancesco Belardo, Enzo M. Li Marzi, Slobodan Simić, JianFeng Wang, 2010, objavljeni znanstveni prispevek na konferenci Ključne besede: grafi, spektri, zaporedje stopenj, graphs, specters, degree sequence
Objavljeno v RUP: 15.10.2015; Ogledov: 2362; Prenosov: 153
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15. A note on a geometric construction of large Cayley graps of given degree and diameterGyörgy Kiss, István Kovács, Klavdija Kutnar, János Ruff, Primož Šparl, 2009, izvirni znanstveni članek Opis: An infinite series and some sporadic examples of large Cayley graphs with given degree and diameter are constructed. The graphs arise from arcs, caps and other objects of finite projective spaces.
Ključne besede: degree, diameter problem, Moore bound, finite projective spaces
Objavljeno v RUP: 15.10.2013; Ogledov: 3343; Prenosov: 69
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17. Almost fully optimized infinite classes of Boolean functions resistant to (fast) algebraic cryptanalysisEnes Pašalić, 2009, objavljeni znanstveni prispevek na konferenci Opis: In this paper the possibilities of an iterative concatenation method towards construction of Boolean functions resistant to algebraic cryptanalysis are investigated. The notion of ▫$\mathcal{AAR}$▫ (Algebraic Attack Resistant) function is introduced as a unified measure of protection against classical algebraic attacks as well as fast algebraic attacks. Then, it is shown that functions that posses the highest resistance to fast algebraic attacks are necessarily of maximum ▫$\mathcal{AI}$▫ (Algebraic Immunity), the notion defined as a minimum degree of functions that annihilate either ▫$f$▫ or ▫$1+f$▫. More precisely, if for any non-annihilating function ▫$g$▫ of degree ▫$e$▫ an optimum degreerelation ▫$e+d \ge n$▫ is satisfied in the product ▫$fg=h$▫ (denoting ▫$deg(h)=d$▫), then the function ▫$f$▫ in ▫$n$▫ variables must have maximum ▫$\mathcal{AI}$▫, i.e. for nonzero function ▫$g$▫ the relation ▫$fg=0$▫ or ▫$(1+f)g=0$▫ implies. The presented theoretical framework allows us to iteratively construct functions with maximum ▫$\mathcal{AI}$▫ satisfying ▫$e+d=n-1$▫, thus almost optimized resistance to fast algebraic cryptanalysis. This infinite class for the first time, apart from almost optimal resistance to algebraic cryptanalysis, in addition generates the functions that possess high nonlinearity (superior to previous constructions) and maximum algebraic degree, thus unifying most of the relevant cryptographic criteria.
Ključne besede: algebraic cryptoanalysis, fast algebraic attacks, algebraic immunity, annihilators, algebraic attack resistant, high degree product, stream ciphers, Boolean function
Objavljeno v RUP: 15.10.2013; Ogledov: 3119; Prenosov: 140
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