Algebraic connectivity of Kronecker products of line graphs

Abstract

Let [Formula: see text] be a tree with [Formula: see text] vertices and [Formula: see text] be its line graph. In this work, we completely characterize the trees for which the algebraic connectivity of [Formula: see text] is equal to [Formula: see text], where × denotes the Kronecker product. We provide a few necessary and sufficient conditions for [Formula: see text] to be Laplacian integral. The algebraic connectivity of [Formula: see text], where [Formula: see text] is a tree of diameter 4 and [Formula: see text]-book graph is discussed.