on the eigenvalues of normal edge-transitive cayley graphs
نویسندگان
چکیده
a graph $gamma$ is said to be vertex-transitive or edge- transitive if the automorphism group of $gamma$ acts transitively on $v(gamma)$ or $e(gamma)$, respectively. let $gamma=cay(g,s)$ be a cayley graph on $g$ relative to $s$. then, $gamma$ is said to be normal edge-transitive, if $n_{aut(gamma)}(g)$ acts transitively on edges. in this paper, the eigenvalues of normal edge-transitive cayley graphs of the groups $d_{2n}$ and $t_{4n}$ are given.
منابع مشابه
On the eigenvalues of normal edge-transitive Cayley graphs
A graph $Gamma$ is said to be vertex-transitive or edge- transitive if the automorphism group of $Gamma$ acts transitively on $V(Gamma)$ or $E(Gamma)$, respectively. Let $Gamma=Cay(G,S)$ be a Cayley graph on $G$ relative to $S$. Then, $Gamma$ is said to be normal edge-transitive, if $N_{Aut(Gamma)}(G)$ acts transitively on edges. In this paper, the eigenvalues of normal edge-tra...
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For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.
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The symmetry properties of mathematical structures are often important for understanding these structures. Graphs sometimes have a large group of symmetries, especially when they have an algebraic construction such as the Cayley graphs. These graphs are constructed from abstract groups and are vertex-transitive and this is the reason for their symmetric appearance. Some Cayley graphs have even ...
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For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and gcd(|H/H ′|, |Z(K)|) = 1 = gcd(|K/K′|, |Z(H)|), we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive. c ⃝ 2014 IAUCTB. All rights reserved.
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عنوان ژورنال:
bulletin of the iranian mathematical societyناشر: iranian mathematical society (ims)
ISSN 1017-060X
دوره 41
شماره 1 2015
کلمات کلیدی
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