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1.
Distance-regular Cayley graphs on dihedral groups
Štefko 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.
Found in: ključnih besedah
Summary of found: ...(if any such exists) from a dihedral difference set satisfying some additional conditions. Finally, all...
Keywords: mathematics, grah theory, distance-regular graph, distance-transitive graph, Cayley graph, dihedral group, dihedrant, difference set
Published: 15.10.2013; Views: 1277; Downloads: 57
URL Full text (0,00 KB)

2.
Distance-regular Cayley graphs on dihedral groups
Primož Potočnik, Štefko Miklavič, 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.
Found in: ključnih besedah
Summary of found: ...(if any such exists) from a dihedral difference set satisfying some additional conditions. Finally, all...
Keywords: mathematics, grah theory, distance-regular graph, distance-transitive graph, Cayley graph, dihedral group, dihedrant, difference set
Published: 10.07.2015; Views: 882; Downloads: 47
URL Full text (0,00 KB)

3.
Karakterizacija posplošnih zlomljenih funkcij in nekatere druge kriptografske teme
Samir Hodžić, 2017, doctoral dissertation

Found in: ključnih besedah
Summary of found: ...bent functions, Zq-bent functions, Gray maps, (relative) difference sets, (generalized) Marioana-McFarland class, stream ciphers, filtering...
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: 09.11.2017; Views: 749; Downloads: 11
URL Full text (0,00 KB)

4.
Full characterization of generalized bent functions as (semi)-bent spaces, their dual, and the Gray image
Samir Hodžić, Wilfried Meidl, Enes Pašalić, 2018, original scientific article

Found in: ključnih besedah
Summary of found: ...maps, dual of generalized bent function, relative difference sets...
Keywords: generalized bent functions, Zq-bent functions, Gray maps, dual of generalized bent function, relative difference sets
Published: 08.06.2018; Views: 404; Downloads: 18
URL Full text (0,00 KB)

5.
Full characterization of generalized bent functions as (semi)-bent spaces, their dual, and the Gray image
Samir Hodžić, Wilfried Meidl, Enes Pašalić, 2018, original scientific article

Found in: ključnih besedah
Summary of found: ...maps, dual of generalized bent function, relative difference sets...
Keywords: generalized bent functions, Zq-bent functions, Gray maps, dual of generalized bent function, relative difference sets
Published: 08.06.2018; Views: 470; Downloads: 21
URL Full text (0,00 KB)

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