Laplacian Spectral Characterization of (Broken) Dandelion Graphs

Abstract

Let $$H(p,tK_{1,m}^ * )$$ be a connected unicyclic graph with p + t(m + 1) vertices obtained from the cycle Cp and t copies of the star K1, m by joining the center of K1, m to each one of t consecutive vertices of the cycle Cp 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.