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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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 |
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| Summary: | 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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| ISSN: | 2768-4202 |