A note on the spectral characterization of dumbbell graphs
A note on the spectral characterization of dumbbell graphs
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DOI：
10.1016/j.laa.2009.06.009
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发表时间：
2009-10
影响因子：
1.1
通讯作者：
Jianfeng Wang;Qiongxiang Huang;Francesco Belardo;E. M. L. Marzi
中科院分区：
文献类型：
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作者：
Jianfeng Wang;Qiongxiang Huang;Francesco Belardo;E. M. L. Marzi
哑铃图用 Da,b,c 表示，是一个双环图，由两个顶点不相交的循环 Ca 和 Cb 组成，并由路径 Pc+3(c⩾-1) 连接，仅具有与两个循环相同的末端顶点。通过对 (r,r+1) 几乎正则图使用新的共谱不变量，我们将证明几乎所有哑铃图（没有环 C4 作为子图）都是由邻接谱确定的。
The dumbbell graph, denoted by Da,b,c, is a bicyclic graph consisting of two vertex-disjoint cycles Caand Cbjoined by a path Pc+3(c⩾-1) having only its end-vertices in common with the two cycles. By using a new cospectral invariant for (r,r+1)-almost regular graphs, we will show that almost all dumbbell graphs (without cycle C4as a subgraph) are determined by the adjacency spectrum.