1. 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: ...... Keywords: mathematics, graph theory, transitive permutation group, 2closed group, squarefree degree, semiregular automorphism, vertextransitive graph Published: 03.04.2017; Views: 921; Downloads: 53 Full text (0,00 KB) 
2. 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: ...... Keywords: mathematics, graph theory, transitive permutation group, 2closed group, semiregular automorphism, vertextransitive graph Published: 03.04.2017; Views: 876; Downloads: 47 Full text (0,00 KB) 
3. 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 Summary of found: ...... 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: 779; Downloads: 111 Full text (0,00 KB) This document has more files! More...

4. Odd automorphism in vertextransitive graphsKlavdija Kutnar, Ademir Hujdurović, Dragan Marušič, 2016, published scientific conference contribution abstract Found in: ključnih besedah Summary of found: ...vertextransitive, graph, odd automorphism, evenclosed, ... Keywords: vertextransitive, graph, odd automorphism, evenclosed Published: 08.08.2016; Views: 992; Downloads: 3 Full text (0,00 KB) 
5. Vertextransitive odd numbersKlavdija Kutnar, Ademir Hujdurović, Dragan Marušič, 2017, published scientific conference contribution abstract (invited lecture) Found in: ključnih besedah Summary of found: ...odd automorphism, evenclosed, vertextransitive, graph, ... Keywords: odd automorphism, evenclosed, vertextransitive, graph Published: 15.11.2017; Views: 409; Downloads: 5 Full text (0,00 KB) 
6. Vertextransitive odd numbersKlavdija Kutnar, Ademir Hujdurović, Dragan Marušič, 2017, published scientific conference contribution abstract (invited lecture) Found in: ključnih besedah Summary of found: ...odd automorphism, evenclosed, vertextransitive, graph, ... Keywords: odd automorphism, evenclosed, vertextransitive, graph Published: 15.11.2017; Views: 409; Downloads: 6 Full text (0,00 KB) 