An improved result on Laplacian spectral ratio of connected graphs

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.

Subject Classification:

• 05C50
• 05C76

Keywords:

• Laplacian eigenvalues
• Ratio
• Tree
• Graph operations