Signless Laplacian determination of a family of double starlike trees
Abstract
UDC 517.9
Two 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 $n\ge 2,$ $p\geq q\geq 2.$
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Copyright (c) 2021 Ali Zeydi Abdian
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