Laplacian Spectral Characterization of (Broken) Dandelion Graphs

Let H ( p t K 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 dande...

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Bibliographic Details
Published in:Indian journal of pure and applied mathematics 2020-09, Vol.51 (3), p.915-933
Main Authors: Yang, Xiaoyun, Wang, Ligong
Format: Article
Language:English
Subjects:
Apexes
Applications of Mathematics
Graph theory
Mathematics
Mathematics and Statistics
Numerical Analysis
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Summary:Let H ( p t K 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 p K 1 m ∗ ) and the broken dandelion graph H ( p t K 1 m ∗ ) (0 < t < p ) are determined by their Laplacian spectra when m ≠ 2 and p is even.
ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-020-0441-5