Tarantula graphs are determined by their Laplacian spectrum
<p class="p1">A graph <em>G</em> is said to be determined by its Laplacian spectrum (DLS) if every graph with the same Laplacian spectrum is isomorphic to <em>G</em>. A graph which is a collection of hexagons (lengths of these cycles can be different) all shar...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia
2021-10-01
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| Series: | Electronic Journal of Graph Theory and Applications |
| Subjects: | |
| Online Access: | https://www.ejgta.org/index.php/ejgta/article/view/796 |
| Summary: | <p class="p1">A graph <em>G</em> is said to be determined by its Laplacian spectrum (DLS) if every graph with the same Laplacian spectrum is isomorphic to <em>G</em>. 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.</p> |
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| ISSN: | 2338-2287 |