### Tarantula graphs are determined by their Laplacian spectrum

#### Abstract

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.

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PDFDOI: http://dx.doi.org/10.5614/ejgta.2021.9.2.14

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