Let \(H(p,tK_{1,m}^ * )\) be a connected unicyclic graph with p + t ( m + 1) vertices obtained from the cycle C _p and t copies of the star K _{1, m} by joining the center of K _{1, m} to each one of t consecutive vertices of the cycle C _p through an edge, respectively. When t = p , the graph is called a dandelion graph and when t ≠ p , the graph is called a broken dandelion graph. In this paper, we prove that the dandelion graph \(H(p,pK_{1,m}^ * )\) and the broken dandelion graph \(H(p,tK_{1,m}^ * )\) (0 < t < p ) are determined by their Laplacian spectra when m ≠ 2 and p is even.

中文翻译：

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（残破的）蒲公英图的拉普拉斯谱特征

让\（H（P，tK_ {1，M} ^ *）\）是一个连通单圈图与 P +吨 （ 米 + 1）从循环中获得顶点 Ç _p 和 吨 星形的副本 ķ _{1， 米} 通过通过边沿将 K _{1， m} 的中心分别连接 到循环 C _p 的 t 个连续顶点中的每个 顶点 。当 t = p时 ，该图称为蒲公英图，而当 t ≠ p时 ，该图称为断蒲公英图。本文证明了蒲公英图\（H（p，pK_ {1，m} ^ *）\）和破碎的蒲公英图\（H（p，tK_ {1，m} ^ *）\）（当 m ≠2并且 p 为偶数时，它们的拉普拉斯光谱确定0 < t < p ） 。