1. On the balanced upper chromatic number of finite projective planesZoltán L. Blázsik, Aart Blokhuis, Štefko Miklavič, Zoltán Lóránt Nagy, Tamás Szőnyi, 2021, original scientific article Keywords: projective planes, balanced upper chromatic number, difference sets, planar functions, probabilistic method Published in RUP: 18.01.2021; Views: 962; Downloads: 35 Link to full text |
2. Full characterization of generalized bent functions as (semi)-bent spaces, their dual, and the Gray imageSamir Hodžić, Wilfried Meidl, Enes Pašalić, 2018, original scientific article Keywords: generalized bent functions, Zq-bent functions, Gray maps, dual of generalized bent function, relative difference sets Published in RUP: 08.06.2018; Views: 1854; Downloads: 100 Link to full text |
3. Karakterizacija posplošnih zlomljenih funkcij in nekatere druge kriptografske teme : doktorska disertacijaSamir Hodžić, 2017, doctoral dissertation Keywords: generalized bent functions, Zq-bent functions, Gray maps, (relative) difference sets, (generalized) Marioana-McFarland class, stream ciphers, filtering generator, guess and determine cryptanalysis, tap positions, (fast) algebraic attacks, algebraic immunity, derivatives, linear structures, planar mappings Published in RUP: 09.11.2017; Views: 2450; Downloads: 56 Link to full text |
4. Distance-regular Cayley graphs on dihedral groupsŠtefko Miklavič, Primož Potočnik, 2005, original scientific article Abstract: The main result of this article is a classification of distance-regular Cayley graphs on dihedral groups. There exist four obvious families of such graphs, which are called trivial. These are: complete graphs, complete bipartite graphs, complete bipartite graphs with the edges of a 1-factor removed, and cycles. It is proved that every non-trivial distance-regular Cayley graph on a dihedral group is bipartite, non-antipodal, has diameter 3 and arises either from a cyclic di#erence set, or possibly (if any such exists) from a dihedral difference set satisfying some additional conditions. Finally, all distance-transitive Cayley graphs on dihedral groups are determined. It transpires that a Cayley graph on a dihedral group is distance-transitive if and only if it is trivial, or isomorphic to the incidence or to the non-incidence graph of a projective space ▫$\mathrm{PG}_{d-1} (d,q)$▫, ▫$d \ge 2$▫, or the unique pair of complementary symmetric designs on 11 vertices. Keywords: mathematics, grah theory, distance-regular graph, distance-transitive graph, Cayley graph, dihedral group, dihedrant, difference set Published in RUP: 10.07.2015; Views: 2453; Downloads: 89 Link to full text |
5. Distance-regular Cayley graphs on dihedral groupsŠtefko Miklavič, Primož Potočnik, 2007, original scientific article Abstract: The main result of this article is a classification of distance-regular Cayley graphs on dihedral groups. There exist four obvious families of such graphs, which are called trivial. These are: complete graphs, complete bipartite graphs, complete bipartite graphs with the edges of a 1-factor removed, and cycles. It is proved that every non-trivial distance-regular Cayley graph on a dihedral group is bipartite, non-antipodal, has diameter 3 and arises either from a cyclic di#erence set, or possibly (if any such exists) from a dihedral difference set satisfying some additional conditions. Finally, all distance-transitive Cayley graphs on dihedral groups are determined. It transpires that a Cayley graph on a dihedral group is distance-transitive if and only if it is trivial, or isomorphic to the incidence or to the non-incidence graph of a projective space ▫$\mathrm{PG}_{d-1} (d,q)$▫, ▫$d \ge 2$▫, or the unique pair of complementary symmetric designs on 11 vertices. Keywords: mathematics, grah theory, distance-regular graph, distance-transitive graph, Cayley graph, dihedral group, dihedrant, difference set Published in RUP: 15.10.2013; Views: 2965; Downloads: 98 Link to full text |