Abstract
LetC(n,k)be the set of all unicyclic graphs withnvertices and cycle lengthk. For anyU∈C(n,k),Uconsists of the (unique) cycle (sayCk) of lengthkand a certain number of trees attached to the vertices ofCkhaving (in total)n-kedges. If there are at most two trees attached to the vertices ofCk, wherekis even, we identify in the class of unicyclic graphs those graphs whose Laplacian spectral radii are minimal.
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