Laplacian Spectral Characterization of Some Unicyclic Graphs

Abstract EN

Let W ( n ; q , m 1 , m 2 ) be the unicyclic graph with n vertices obtained by attaching two paths of lengths m 1 and m 2 at two adjacent vertices of cycle C q .

Let U ( n ; q , m 1 , m 2 , … , m s ) be the unicyclic graph with n vertices obtained by attaching s paths of lengths m 1 , m 2 , … , m s at the same vertex of cycle C q .

In this paper, we prove that W ( n ; q , m 1 , m 2 ) and U ( n ; q , m 1 , m 2 , … , m s ) are determined by their Laplacian spectra when q is even.