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Creators/Authors contains: "Huang, Qiongxiang"

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  1. ; ; (, The Electronic journal of combinatorics)
    Let $$\Gamma$$ be a finite group acting transitively on $$[n]=\{1,2,\ldots,n\}$$, and let $$G=\mathrm{Cay}(\Gamma,T)$$ be a Cayley graph of $$\Gamma$$. The graph $$G$$ is called normal if $$T$$ is closed under conjugation. In this paper, we obtain an upper bound for \textcolor[rgb]{0,0,1}{the second (largest) eigenvalue} of the adjacency matrix of the graph $$G$$ in terms of the second eigenvalues of certain subgraphs of $$G$$ (see Theorem 2.6). Using this result, we develop a recursive method to determine the second eigenvalues of certain Cayley graphs of $$S_n$$ and we determine the second eigenvalues of a majority of the connected normal Cayley graphs (and some of their subgraphs) of $$S_n$$ with $$\max_{\tau\in T}|\mathrm{supp}(\tau)|\leq 5$$, where $$\mathrm{supp}(\tau)$$ is the set of points in $[n]$ non-fixed by $$\tau$$. 
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    Accepted Manuscript Full Text Available
  2. ; ; (, The Electronic journal of combinatorics)
    Let $$\Gamma$$ be a finite group acting transitively on $$[n]=\{1,2,\ldots,n\}$$, and let $$G=\mathrm{Cay}(\Gamma,T)$$ be a Cayley graph of $$\Gamma$$. The graph $$G$$ is called normal if $$T$$ is closed under conjugation. In this paper, we obtain an upper bound for \textcolor[rgb]{0,0,1}{the second (largest) eigenvalue} of the adjacency matrix of the graph $$G$$ in terms of the second eigenvalues of certain subgraphs of $$G$$ (see Theorem 2.6). Using this result, we develop a recursive method to determine the second eigenvalues of certain Cayley graphs of $$S_n$$ and we determine the second eigenvalues of a majority of the connected normal Cayley graphs (and some of their subgraphs) of $$S_n$$ with $$\max_{\tau\in T}|\mathrm{supp}(\tau)|\leq 5$$, where $$\mathrm{supp}(\tau)$$ is the set of points in $[n]$ non-fixed by $$\tau$$. 
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    Accepted Manuscript Full Text Available
  3. ; ; (, The Electronic Journal of Combinatorics)
    Let $$G$$ be a finite group acting transitively on $$[n]=\{1,2,\ldots,n\}$$, and  let $$\Gamma=\mathrm{Cay}(G,T)$$ be a Cayley graph of $$G$$. The graph $$\Gamma$$ is called  normal if $$T$$ is closed under conjugation. In this paper, we obtain an upper bound for the second (largest) eigenvalue of the adjacency matrix of the graph $$\Gamma$$ in terms of the second eigenvalues of certain subgraphs of $$\Gamma$$. Using this result, we develop a recursive method to  determine the second eigenvalues of certain  Cayley graphs of $$S_n$$, and we determine the second eigenvalues  of a majority of the connected normal Cayley graphs (and some of their subgraphs) of $$S_n$$  with  $$\max_{\tau\in T}|\mathrm{supp}(\tau)|\leqslant 5$$, where $$\mathrm{supp}(\tau)$$ is the set of points in $[n]$ non-fixed by $$\tau$$. 
    more » « less
    Full Text Available