The spectral characterization of ∞-graphs
The spectral characterization of ∞-graphs
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DOI：
10.1016/j.laa.2012.04.013
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发表时间：
2012-10
影响因子：
1.1
通讯作者：
Fenjin Liu;Qiongxiang Huang;Jianfeng Wang;Qinghai Liu
中科院分区：
文献类型：
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作者：
Fenjin Liu;Qiongxiang Huang;Jianfeng Wang;Qinghai Liu
∞-图 B(r,s) 是由两个循环 Cr+1 和 Cs+1 组成的图，只有一个公共顶点。 Fan和Luo在定理4.4[8]中声称，如果一个∞图不包含环C4，那么它是由它的邻接谱决定的。然而，根据定理6.3[16]我们发现定理4.4[8]的结果并不完全正确。在本文中，我们证明当且仅当 s≠r+2 时 B(r,s)(s⩾r>7) 是 DAS，并且当 s=r+2 时 B(r,s)(s⩾r>7) 具有唯一的共谱伴侣。
A ∞-graph B(r,s) is a graph consisting of two cycles Cr+1and Cs+1with just a vertex in common. Fan and Luo in Theorem 4.4 [8] alleged that a ∞-graph is determined by its adjacency spectrum if it contains no cycle C4. However, according to Theorem 6.3 [16] we find that the result in Theorem 4.4 [8] is not completely correct. In this paper, we prove that B(r,s)(s⩾r>7) is DAS if and only if s≠=r+2, and B(r,s)(s⩾r>7) has a unique cospectral mate if s=r+2.