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Let $$\fancyscript{T}_{n,\gamma }$$ T n , γ be the collection of all $$n$$ n -vertex trees with domination number $$\gamma $$ γ . In this paper, the first-, second- and third-smallest Laplacian permanents of trees in $$\fancyscript{T}_{n,\gamma }$$ T n , γ are determined, respectively. Moreover, the corresponding extremal graphs are characterized.
Let $${\fancyscript{U}_{n}}$$ be the set of n-vertex unicyclic graphs, $${\fancyscript{U}_n^d}$$ be the set of n-vertex unicyclic graphs of diameter d. In this paper we determine the second-minimum value of signless Laplacian permanent of graphs among $${\fancyscript{U}_{n}}$$ ; as well we obtain the lower bound for the signless Laplacian permanent of graphs in $${\fancyscript{U}_{n}^d}$$...
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