Signless Laplacian determination of a family of double starlike trees

• Datum: 2021
• Hauptverfasser: Sharafdini , R., Abdian, A. Z., Behmaram, A., к, Zeydi Abdian, Ali, ь
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2021
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/634
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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 $n\ge 2,$ $p\geq q\geq 2.$