An improved result on Laplacian spectral ratio of connected graphs. Issue 4 (19th May 2021) - Lin, Zhen; Miao, Lianying
Abstract: The Laplacian spectral ratio of a connected graph G, denoted by r L ( G ), is defined as the quotient between the largest and second smallest Laplacian eigenvalues of G . In 2002, Barahona and Pecora showed that rL ( G ) play an important role in the network synchronization control. In this paper, we obtain a result on the Laplacian spectral ratio of trees, which improve the known result of You and Liu [Z. You, B. Liu, On the Laplacian spectral ratio of connected graphs, Appl. Math. Lett. 25(2012)1245-1250]. Moreover, some graph operations on Laplacian spectral ratio are given.