We determine the graph with the largest signless Laplacian spectral radius among all unicyclic graphs with fixed matching number.

The graph with the largest signless Laplacian spectral radius among all bicyclic graphs with perfect matchings is determined.

Let q (G) denote the spectral radius of the signless Laplacian matrix of a graph G, also known as the Q-index of G. The aim of this note is to study a general extremal problem: How large can q (G) be when G belongs to an abstract graph property? Even knowing very little about the graph property, this paper shows that useful conclusions about the asymptotics of q (G) can be made, which turn out ...

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Let U(n, g) and B(n, g) be the set of unicyclic graphs and bicyclic graphs on n vertices with girth g, respectively. Let B1(n, g) be the subclass of B(n, g) consisting of all bicyclic graphs with two edge-disjoint cycles and B2(n, g) = B(n, g)\B1(n, g). This paper determines the unique graph with the maximal signless Laplacian spectral radius among all graphs in U(n, g) and B(n, g), respectivel...