Discrepancy and eigenvalues of Cayley graphs
نویسندگان
چکیده
منابع مشابه
Discrepancy and Eigenvalues of Cayley Graphs
We consider quasirandom properties for Cayley graphs of finite abelian groups. In particular, we show that having uniform edgedistribution (i.e., small discrepancy) and having large eigenvalue gap are equivalent properties for Cayley graphs, even if they are sparse. This positively answers a question of Chung and Graham [“Sparse quasi-random graphs”, Combinatorica 22 (2002), no. 2, 217–244] for...
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In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...
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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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Let $Gamma$ be a graph with adjacency eigenvalues $lambda_1leqlambda_2leqldotsleqlambda_n$. Then the energy of $Gamma$, a concept defined in 1978 by Gutman, is defined as $mathcal{E}(G)=sum_{i=1}^n|lambda_i|$. Also the Estrada index of $Gamma$, which is defined in 2000 by Ernesto Estrada, is defined as $EE(Gamma)=sum_{i=1}^ne^{lambda_i}$. In this paper, we compute the eigen...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2016
ISSN: 0011-4642,1572-9141
DOI: 10.1007/s10587-016-0302-x