Relation between the matching number and the second largest distance Laplacian eigenvalue of a graph

Abstract

Let G be a connected simple graph with matching number m(G). The second largest distance Laplacian eigenvalue of G is denoted by ∂2(G). In this paper, we investigate the relation between the matching number and the second largest distance Laplacian eigenvalue of G, establishing the lower bounds of ∂2(G) in terms of m(G). Moreover, all the extremal graphs attaining the lower bounds are completely characterized.