On the multiplicity of Laplacian eigenvalues for unicyclic graphs
Fei Wen, Qiongxiang Huang (2022)
Czechoslovak Mathematical Journal
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Let be a connected graph of order and a unicyclic graph with the same order. We firstly give a sharp bound for , the multiplicity of a Laplacian eigenvalue of . As a straightforward result, . We then provide two graph operations (i.e., grafting and shifting) on graph for which the value of is nondecreasing. As applications, we get the distribution of for unicyclic graphs on vertices. Moreover, for the two largest possible values of , the corresponding graphs are...