Incidence and Laplacian matrices of wheel graphs and their inverses
It has been an open problem to find the Moore-Penrose inverses of the incidence, Laplacian, and signless Laplacian matrices of families of graphs except trees and unicyclic graphs. Since the inverse formulas for an odd unicyclic graph and an even unicyclic graph are quite different, we consider whe...
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| Format: | Article |
| Language: | English |
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American Journal of Combinatorics
2023-07-01
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| Series: | The American Journal of Combinatorics |
| Subjects: | |
| Online Access: | https://ajcombinatorics.org/ojs/index.php/AmJC/article/view/9 |
| _version_ | 1826585493859467264 |
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| author | Jerad Ipsen Sudipta Mallik |
| author_facet | Jerad Ipsen Sudipta Mallik |
| author_sort | Jerad Ipsen |
| collection | DOAJ |
| description |
It has been an open problem to find the Moore-Penrose inverses of the incidence, Laplacian, and signless Laplacian matrices of families of graphs except trees and unicyclic graphs. Since the inverse formulas for an odd unicyclic graph and an even unicyclic graph are quite different, we consider wheel graphs as they are formed from odd or even cycles. In this article we solve the open problem for wheel graphs. This work has an interesting connection to inverses of circulant matrices.
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| first_indexed | 2025-03-14T15:54:32Z |
| format | Article |
| id | doaj.art-d2c9e4d66bc245a1a2f20b9847b13fc6 |
| institution | Directory Open Access Journal |
| issn | 2768-4202 |
| language | English |
| last_indexed | 2025-03-14T15:54:32Z |
| publishDate | 2023-07-01 |
| publisher | American Journal of Combinatorics |
| record_format | Article |
| series | The American Journal of Combinatorics |
| spelling | doaj.art-d2c9e4d66bc245a1a2f20b9847b13fc62025-02-24T02:26:50ZengAmerican Journal of CombinatoricsThe American Journal of Combinatorics2768-42022023-07-01210.63151/amjc.v2i.9Incidence and Laplacian matrices of wheel graphs and their inversesJerad IpsenSudipta Mallik It has been an open problem to find the Moore-Penrose inverses of the incidence, Laplacian, and signless Laplacian matrices of families of graphs except trees and unicyclic graphs. Since the inverse formulas for an odd unicyclic graph and an even unicyclic graph are quite different, we consider wheel graphs as they are formed from odd or even cycles. In this article we solve the open problem for wheel graphs. This work has an interesting connection to inverses of circulant matrices. https://ajcombinatorics.org/ojs/index.php/AmJC/article/view/9Moore-Penrose inverseLaplacian matrixIncidence matrixCirculant matrixWheel graph |
| spellingShingle | Jerad Ipsen Sudipta Mallik Incidence and Laplacian matrices of wheel graphs and their inverses The American Journal of Combinatorics Moore-Penrose inverse Laplacian matrix Incidence matrix Circulant matrix Wheel graph |
| title | Incidence and Laplacian matrices of wheel graphs and their inverses |
| title_full | Incidence and Laplacian matrices of wheel graphs and their inverses |
| title_fullStr | Incidence and Laplacian matrices of wheel graphs and their inverses |
| title_full_unstemmed | Incidence and Laplacian matrices of wheel graphs and their inverses |
| title_short | Incidence and Laplacian matrices of wheel graphs and their inverses |
| title_sort | incidence and laplacian matrices of wheel graphs and their inverses |
| topic | Moore-Penrose inverse Laplacian matrix Incidence matrix Circulant matrix Wheel graph |
| url | https://ajcombinatorics.org/ojs/index.php/AmJC/article/view/9 |
| work_keys_str_mv | AT jeradipsen incidenceandlaplacianmatricesofwheelgraphsandtheirinverses AT sudiptamallik incidenceandlaplacianmatricesofwheelgraphsandtheirinverses |