Laplacian Spectral Characterization of (Broken) Dandelion Graphs

Let H(ptK1m∗) 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(ppK1m∗) and the broken dandelion graph H(ptK1m∗) (0 < t < p) are determined by their Laplacian spectra when m ≠ 2 and p is even.