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 |
| _version_ | 1818217426785927168 |
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| author | Reza Sharafdini Ali Zeydi Abdian |
| author_facet | Reza Sharafdini Ali Zeydi Abdian |
| author_sort | Reza Sharafdini |
| collection | DOAJ |
| description | <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> |
| first_indexed | 2024-12-12T07:07:41Z |
| format | Article |
| id | doaj.art-561498d43bf4407a97588e98019923d7 |
| institution | Directory Open Access Journal |
| issn | 2338-2287 |
| language | English |
| last_indexed | 2024-12-12T07:07:41Z |
| publishDate | 2021-10-01 |
| publisher | Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia |
| record_format | Article |
| series | Electronic Journal of Graph Theory and Applications |
| spelling | doaj.art-561498d43bf4407a97588e98019923d72022-12-22T00:33:42ZengIndonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), IndonesiaElectronic Journal of Graph Theory and Applications2338-22872021-10-019241943110.5614/ejgta.2021.9.2.14230Tarantula graphs are determined by their Laplacian spectrumReza Sharafdini0Ali Zeydi Abdian1Department of Mathematics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr 75169, IranDepartment of Mathematical Sciences, Lorestan University, College of Science, Lorestan, Khoramabad, Iran<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>https://www.ejgta.org/index.php/ejgta/article/view/796tarantula graphlaplacian matrixlaplacian spectruml-cospectral |
| spellingShingle | Reza Sharafdini Ali Zeydi Abdian Tarantula graphs are determined by their Laplacian spectrum Electronic Journal of Graph Theory and Applications tarantula graph laplacian matrix laplacian spectrum l-cospectral |
| title | Tarantula graphs are determined by their Laplacian spectrum |
| title_full | Tarantula graphs are determined by their Laplacian spectrum |
| title_fullStr | Tarantula graphs are determined by their Laplacian spectrum |
| title_full_unstemmed | Tarantula graphs are determined by their Laplacian spectrum |
| title_short | Tarantula graphs are determined by their Laplacian spectrum |
| title_sort | tarantula graphs are determined by their laplacian spectrum |
| topic | tarantula graph laplacian matrix laplacian spectrum l-cospectral |
| url | https://www.ejgta.org/index.php/ejgta/article/view/796 |
| work_keys_str_mv | AT rezasharafdini tarantulagraphsaredeterminedbytheirlaplacianspectrum AT alizeydiabdian tarantulagraphsaredeterminedbytheirlaplacianspectrum |