Cayley graphs with few automorphisms
نویسندگان
چکیده
منابع مشابه
On colour-preserving automorphisms of Cayley graphs
We study the automorphisms of a Cayley graph that preserve its natural edge-colouring. More precisely, we are interested in groups G, such that every such automorphism of every connected Cayley graph on G has a very simple form: the composition of a left-translation and a group automorphism. We find classes of groups that have this property, and we determine the orders of all groups that do not...
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Let G be a group and CayP (G) < Sym(G) be the subgroup of all permutations that induce graph automorphisms on every Cayley graph of G. The group G is graphically abelian if the map ν : g → g−1 belongs to CayP (G); these groups have been classified. Also G is irregular if there exists σ ∈ CayP (G) such that σ = 1G, σ(1) = 1 and σ = ν. We show G is irregular if and only if G = Dic(A, I); every no...
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Let S be a set of transpositions such that the girth of the transposition graph of S is at least 5. It is shown that the automorphism group of the Cayley graph of the permutation group H generated by S is the semidirect product R(H) ⋊ Aut(H,S), where R(H) is the right regular representation of H and Aut(H,S) is the set of automorphisms of H that fixes S setwise. Furthermore, if the connected co...
متن کاملCayley graphs - Cayley nets
It is, however, not clear how to choose the generators to produce special graphs. We know many topologies and their generators, but many more may be constructed in the future, having better properties (in terms of diameter, nodal degree and connectivity) than for instance the hypercube. I will present several graphs which connect rings using the generator g 1 and some additional generators.
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2020
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-020-00956-1