Spectral Determination of some Chemical Graphs

Changjiang Bu, Jiang Zhou, Hongbo Li

Let $T^k_n$ denote the caterpillar obtained by attaching $k$ pendant edges at two pendant vertices of the path $P_n$ and two pendant edges at the other vertices of $P_n$. It is proved that $T^k_n$ is determined by its signless Laplacian spectrum when $k=2$ or $3$, while $T^2_n$ by its Laplacian spectrum.