Ordering cacti with signless Laplacian spread

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Zhen Lin
Shu-Guang Guo


A cactus is a connected graph in which any two cycles have at most one vertex in common. The signless Laplacian spread of a graph is defined as the difference between the largest eigenvalue and the smallest eigenvalue of the associated signless Laplacian matrix. In this paper, all cacti of order n with signless Laplacian spread greater than or equal to n - 1/2 are determined.

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