TY - JOUR AU - R. Sharafdini AU - A. Z. Abdian AU - A. Behmaram PY - 2021/09/16 Y2 - 2024/03/28 TI - Signless Laplacian determination of a family of double starlike trees JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 73 IS - 9 SE - Research articles DO - 10.37863/umzh.v73i9.634 UR - https://umj.imath.kiev.ua/index.php/umj/article/view/634 AB - UDC 517.9Two graphs are said to be $Q$-cospectral if they have the same signless Laplacian spectrum.A graph is said to be DQS if there are no other nonisomorphic graphs $Q$-cospectral with it. A tree is called double starlike if it has exactly two vertices of degree greater than 2.Let $H_n(p,q)$ with $n \ge 2,$ $p \geq q \geq 2$ denote the double starlike tree obtained by attaching $p$ pendant vertices to one pendant vertex of the path $P_n$ and $q$ pendant vertices to the other pendant vertex of $P_n.$ In this paper, we prove that $H_n(p,q)$ is  DQS for $n\ge 2,$ $p\geq q\geq 2.$  ER -