Abstract
The kth power of a graph G, denoted by Gk, is the graph with the same vertex set as G, such that two vertices are adjacent in Gk if and only if their distance is at most k in G. In this paper, we give bounds on the first two largest Laplacian eigenvalues of the second power of a general graph, and on the second power of a tree. We also give a Nordhaus–Gaddum-type inequality for the Laplacian spectral radius of G2.
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