Mathematics (Apr 2022)
A Lower Bound for the Distance Laplacian Spectral Radius of Bipartite Graphs with Given Diameter
Abstract
Let G be a connected, undirected and simple graph. The distance Laplacian matrix L(G) is defined as L(G)=diag(Tr)−D(G), where D(G) denotes the distance matrix of G and diag(Tr) denotes a diagonal matrix of the vertex transmissions. Denote by ρL(G) the distance Laplacian spectral radius of G. In this paper, we determine a lower bound of the distance Laplacian spectral radius of the n-vertex bipartite graphs with diameter 4. We characterize the extremal graphs attaining this lower bound.
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