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.
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This work was supported by the National Natural Science Foundation of China (No. 11871398), the Nature Science Basic Research Plan in Shannxi Province of China (Program No. 2018JM1032) and the National College Students Innovation and Entrepreneurship Training Program (No. 201610699011).
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Yang, X., Wang, L. Laplacian Spectral Characterization of (Broken) Dandelion Graphs. Indian J Pure Appl Math 51, 915–933 (2020). https://doi.org/10.1007/s13226-020-0441-5
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DOI: https://doi.org/10.1007/s13226-020-0441-5