Algebraic connectivity of Kronecker products of line graphs.

Let X be a tree with n vertices and L (X) be its line graph. In this work, we completely characterize the trees for which the algebraic connectivity of L (X) × K m is equal to m − 1 , where × denotes the Kronecker product. We provide a few necessary and sufficient conditions for L (X) × K m to be Laplacian integral. The algebraic connectivity of L (X) × K m , where X is a tree of diameter 4 and k -book graph is discussed. [ABSTRACT FROM AUTHOR]