Abelian groups with isomorphic intersection graphs
نویسندگان
چکیده
منابع مشابه
Which Finitely Generated Abelian Groups Admit Isomorphic Cayley Graphs?
We show that Cayley graphs of finitely generated Abelian groups are rather rigid. As a consequence we obtain that two finitely generated Abelian groups admit isomorphic Cayley graphs if and only if they have the same rank and their torsion parts have the same cardinality. The proof uses only elementary arguments and is formulated in a geometric language.
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let $g$ be a finite group with the identity $e$. the subgroup intersection graph $gamma_{si}(g)$ of $g$ is the graph with vertex set $v(gamma_{si}(g)) = g-e$ and two distinct vertices $x$ and $y$ are adjacent in $gamma_{si}(g)$ if and only if $|leftlangle xrightrangle capleftlangle yrightrangle|>1$, where $leftlangle xrightrangle $ is the cyclic subgroup of $g$ generated by $xin g$. in th...
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Abstract : We call a Cayley graph Γ = Cay (G, S) normal for G, if the right regular representation R(G) of G is normal in the full automorphism group of Aut(Γ). In this paper, a classification of all non-normal Cayley graphs of finite abelian group with valency 6 was presented.
متن کاملNORMAL 6-VALENT CLAYEY GRAPHS OF ABELIAN GROUPS
We call a Clayey graph Γ = Cay(G, S) normal for G, if the right regular representation R(G) of G is normal in the full automorphism group of Aunt(Γ). in this paper, we give a classification of all non-normal Clayey graphs of finite abelian group with valency 6.
متن کاملIsomorphic Cayley Graphs on different Groups
The issue of when two Cayley digraphs on different abelian groups of prime power order can be isomorphic is examined. This had previously been determined by Anne Joseph for squares of primes; her results are extended. 1 Preliminaries We begin with some essential definitions. For many of these results, the lemmata and proofs used are direct extensions of those in Joseph’s paper [1]. Although we ...
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ژورنال
عنوان ژورنال: Acta Mathematica Hungarica
سال: 2015
ISSN: 0236-5294,1588-2632
DOI: 10.1007/s10474-015-0486-9