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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Ali Zeydi Abdian
Department of Mathematical Sciences, Lorestan University, College of Science, Lorestan, Khoramabad, Iran
Electrical & Electronics Engineering

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Tarantula graphs are determined by their Laplacian spectrum Reza Sharafdini; Ali Zeydi Abdian
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2021.9.2.14

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.
Co-Authors Reza Sharafdini