Tarantula graphs are determined by their Laplacian spectrum

Reza Sharafdini (Department of Mathematics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr 75169, Iran)
Ali Zeydi Abdian (Department of Mathematical Sciences, Lorestan University, College of Science, Lorestan, Khoramabad, Iran)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications

A graph G is said to be determined by its Laplacian spectrum (DLS) if every graph with the same Laplacian spectrum is isomorphic to G. A graph which is a collection of hexagons (lengths of these cycles can be different) all sharing precisely one vertex is called a spinner graph. A tree with exactly one vertex of degree greater than 2 is called a starlike tree. If a spinner graph and a starlike tree are joined by merging their vertices of degree greater than 2, then the resulting graph is called a tarantula graph. It is known that spinner graphs and starlike trees are DLS.  In this paper, we prove that tarantula graphs are determined by their Laplacian spectrum.