@article{Li2026, 
author = {Wenjing Li and Yiwei Zhang and Ying Wang},
title = {On the characteristic polynomials of Dutch windmill graphs and their applications},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {16697-16711},
keywords = {adjacency spectrum, Laplacian spectrum, signless Laplacian spectrum, graph energy, Laplacian energy, signless Laplacian energy, Dutch windmill graph},
url = {https://www.sciopen.com/article/10.3934/math.2026685},
doi = {10.3934/math.2026685},
abstract = {The Dutch windmill graph        D    p    q   is formed by    q cycles of length    p sharing a common vertex        v    0  . In this paper, we derive closed-form expressions for the characteristic polynomials—specifically, the adjacency polynomial        Φ    A    (      D    p    q    ,  λ  ), the Laplacian polynomial        Φ    L    (      D    p    q    ,  μ  ), and the signless Laplacian polynomial        Φ                  L        +              (      D    p    q    ,  ν  ) —of this family of graphs. As a direct consequence, we compute the exact values of the graph energy, Laplacian energy, and signless Laplacian energy of Dutch windmill graphs.}
}