81. Minimal normal subgroups of transitive permutation groups of squarefree degreeAleksander Malnič, Dragan Marušič, Edward Dobson, Lewis A. Nowitz, 2007, original scientific article Abstract: It is shown that a minimal normal subgroup of a transitive permutation group of squarefree 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 2closed permutation group of squarefree degree in its induced action is simple. As an almost immediate consequence, it follows that a 2closed transitive permutation group of squarefree degree contains a semiregular element of prime order, thus giving a partial affirmative answer to the conjecture that all 2closed transitive permutation groups contain such an element (see [D. Marušic, On vertex symmetric digraphs,Discrete Math. 36 (1981) 6981; P.J. Cameron (Ed.), Problems from the fifteenth British combinatorial conference, Discrete Math. 167/168 (1997) 605615]). Found in: ključnih besedah Summary of found: ...mathematics, graph theory, transitive permutation group, 2closed group, squarefree... Keywords: mathematics, graph theory, transitive permutation group, 2closed group, squarefree degree, semiregular automorphism, vertextransitive graph Published: 03.04.2017; Views: 991; Downloads: 57 Full text (0,00 KB) 
82. Symmetry structure of bicirculantsBoštjan Frelih, Primož Šparl, Aleksander Malnič, Dragan Marušič, 2007, original scientific article Abstract: An ▫$n$▫bicirculant is a graph having an automorphism with two orbits of length ▫$n$▫ and no other orbits. Symmetry properties of ▫$p$▫bicirculants, ▫$p$▫ a prime, are extensively studied. In particular, the actions of their automorphism groups are described in detail in terms of certain algebraic representation of such graphs. Found in: ključnih besedah Summary of found: ...An ▫$n$▫bicirculant is a graph having an automorphism with two orbits of... Keywords: mathematics, graph theory, graph, circulant, bicirculant, automorphism group Published: 03.04.2017; Views: 1121; Downloads: 61 Full text (0,00 KB) 
83. On strongly regular bicirculantsDragan Marušič, Aleksander Malnič, Primož Šparl, 2007, original scientific article Abstract: An ▫$n$▫bicirculantis a graph having an automorphism with two orbits of length ▫$n$▫ and no other orbits. This article deals with strongly regular bicirculants. It is known that for a nontrivial strongly regular ▫$n$▫bicirculant, ▫$n$▫ odd, there exists a positive integer m such that ▫$n=2m^2+2m+1▫$. Only three nontrivial examples have been known previously, namely, for ▫$m=1,2$▫ and 4. Case ▫$m=1$▫ gives rise to the Petersen graph and its complement, while the graphs arising from cases ▫$m=2$▫ and ▫$m=4$▫ are associated with certain Steiner systems. Similarly, if ▫$n$▫ is even, then ▫$n=2m^2$▫ for some ▫$m \ge 2$▫. Apart from a pair of complementary strongly regular 8bicirculants, no other example seems to be known. A necessary condition for the existence of a strongly regular vertextransitive ▫$p$▫bicirculant, ▫$p$▫ a prime, is obtained here. In addition, three new strongly regular bicirculants having 50, 82 and 122 vertices corresponding, respectively, to ▫$m=3,4$▫ and 5 above, are presented. These graphs are not associated with any Steiner system, and together with their complements form the first known pairs of complementary strongly regular bicirculants which are vertextransitive but not edgetransitive. Found in: ključnih besedah Summary of found: ...An ▫$n$▫bicirculantis a graph having an automorphism with two orbits of... Keywords: mathematics, graph theory, graph, circulant, bicirculant, automorphism group Published: 03.04.2017; Views: 1241; Downloads: 56 Full text (0,00 KB) 
84. Semiregular automorphisms of vertextransitive graphs of certain valenciesDragan Marušič, Edward Dobson, Aleksander Malnič, Lewis A. Nowitz, 2007, original scientific article Abstract: It is shown that a vertextransitive graph of valency ▫$p+1$▫, ▫$p$▫ a prime, admitting a transitive action of a ▫$\{2,p\}$▫group, has a nonidentity semiregular automorphism. As a consequence, it is proved that a quartic vertextransitive graph has a nonidentity semiregular automorphism, thus giving a partial affirmative answer to the conjecture that all vertextransitive graphs have such an automorphism and, more generally, that all 2closed transitive permutation groups contain such an element (see [D. Marušic, On vertex symmetric digraphs, Discrete Math. 36 (1981) 6981; P.J. Cameron (Ed.), Problems from the Fifteenth British Combinatorial Conference, Discrete Math. 167/168 (1997) 605615]). Found in: ključnih besedah Summary of found: ...It is shown that a vertextransitive graph of valency ▫$p+1$▫, ▫$p$▫ a prime, admitting... Keywords: mathematics, graph theory, transitive permutation group, 2closed group, semiregular automorphism, vertextransitive graph Published: 03.04.2017; Views: 990; Downloads: 51 Full text (0,00 KB) 
85. Semisymmetric elementary abelian covers of the MöbiusKantor graphAleksander Malnič, Štefko Miklavič, Primož Potočnik, Dragan Marušič, 2007, original scientific article Abstract: Let ▫$\wp_N : \tilde{X} \to X$▫ be a regular covering projection of connected graphs with the group of covering transformations isomorphic to ▫$N$▫. If ▫$N$▫ is an elementary abelian ▫$p$▫group, then the projection ▫$\wp_N$▫ is called ▫$p$▫elementary abelian. The projection ▫$\wp_N$▫ is vertextransitive (edgetransitive) if some vertextransitive (edgetransitive) subgroup of Aut ▫$X$▫ lifts along ▫$\wp_N$▫, and semisymmetric if it is edge but not vertextransitive. The projection ▫$\wp_N$▫ is minimal semisymmetric if ▫$\wp_N$▫ cannot be written as a composition ▫$\wp_N = \wp \circ \wp_M$▫ of two (nontrivial) regular covering projections, where ▫$\pw_M$▫ is semisymmetric. Finding elementary abelian covering projections can be grasped combinatorially via a linear representation of automorphisms acting on the first homology group of the graph. The method essentially reduces to finding invariant subspaces of matrix groups over prime fields (see [A. Malnic, D. Marušic, P. Potocnik, Elementary abelian covers of graphs, J. Algebraic Combin. 20 (2004) 7197]). In this paper, all pairwise nonisomorphic minimal semisymmetric elementary abelian regular covering projections of the MöbiusKantor graph, the Generalized Petersen graph GP(8,3), are constructed. No such covers exist for ▫$p=2$▫. Otherwise, the number of such covering projections is equal to ▫$(p1)/4$▫ and ▫$1+(p1)/4$▫ in cases ▫$p \equiv 5,9,13,17,21 \pmod{24}$▫ and ▫$p \equiv 1 \pmod{24}$▫, respectively, and to ▫$(p+1)/4$▫ and ▫$1+(p+1)/4$▫ in cases ▫$p \equiv 3,7,11,15,23 \pmod{24}$▫ and ▫$p \equiv 19 \pmod{24}$▫, respectively. For each such covering projection the voltage rules generating the corresponding covers are displayed explicitly. Found in: ključnih besedah Keywords: mathematics, graph theory, graph, covering projection, lifting automorphisms, homology group, group representation, matrix group, invariant subspaces Published: 03.04.2017; Views: 891; Downloads: 55 Full text (0,00 KB) 
86. Additive rankone nonincreasing maps on Hermitian matrices over the field GF(2[sup]2)Marko Orel, Bojan Kuzma, 2009, original scientific article Abstract: A complete classification of additive rankone nonincreasing maps on hermitian matrices over Galois field ▫$GF(2^2)$▫ is obtained. This field is special and was not covered in a previous paper. As a consequence, some known applications, like the classification of additive rankadditivity preserving maps, are extended to arbitrary fields. An application concerning the preservers of hermitian varieties is also presented. Found in: ključnih besedah Keywords: mathematics, linear algebra, additive preserver, hermitian matrices, rank, Galois field, weak homomorphism of a graph Published: 03.04.2017; Views: 978; Downloads: 31 Full text (0,00 KB) This document has more files! More...

87. On maximal distances in a commuting graphBojan Kuzma, Polona Oblak, Gregor Dolinar, 2012, original scientific article Abstract: It is shown that matrices over algebraically closed fields that are farthest apart in the commuting graph must be nonderogatory. Rankone matrices and diagonalizable matrices are also characterized in terms of the commuting graph. Found in: ključnih besedah Keywords: matematika, linearna algebra, teorija grafov, komutirajoči grafi, matrična algebra, algebraično zaprt obseg, centralizator, razdalja v grafih, mathematics, linear algebra, graph theory, commuting graph, matrix algebra, algebraically closed field, centralizer, distance in graphs Published: 03.04.2017; Views: 852; Downloads: 129 Full text (0,00 KB) This document has more files! More...

88. On generalizations of the Petersen graph and the Coxeter graphMarko Orel, 2015, original scientific article Found in: ključnih besedah Keywords: Petersenov graf, Coexerjev graf, hermitske matrike, simetrične matrike, Coexter graph, Petersen graph, Hermitian matrix, symmetric matrix Published: 03.04.2017; Views: 829; Downloads: 40 Full text (0,00 KB) 
89. Generalized cagesRobert Jajcay, Marko Boben, Tomaž Pisanski, 2015, original scientific article Found in: ključnih besedah Summary of found: ...cage, graph, isomorphism, ... Keywords: cage, graph, isomorphism Published: 03.04.2017; Views: 737; Downloads: 26 Full text (0,00 KB) 
90. Groups that are transitive on all partitions of a given shapeEdward Dobson, Aleksander Malnič, 2015, original scientific article Found in: ključnih besedah Summary of found: ...transitive group, ordered partition, unordered partition, Johnson graph, Cayley graph, ... Keywords: transitive group, ordered partition, unordered partition, Johnson graph, Cayley graph Published: 03.04.2017; Views: 948; Downloads: 104 Full text (0,00 KB) 