On the second minimum algebraic connectivity of the graphs whose complements are trees

Peer review under responsibility of Kalasalingam University.

Abstract

For a graph $\Gamma$ the algebraic connectivity denoted by $a\left(\Gamma \right)$, is the second smallest eigenvalue of the Laplacian matrix of $\Gamma$. In Jiang et al. (2015), proved a unique graph with first minimum algebraic connectivity among the graphs which belong to a class of graphs whose complements are trees. In this paper, we characterize the unique graph with second minimum algebraic connectivity in the same aforesaid class of graphs.

Keywords:

• Laplacian matrix
• Algebraic connectivity
• Complement of trees

Notes

Peer review under responsibility of Kalasalingam University.