Iterated line graphs with only negative eigenvalues $-2$, their complements and energy
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918213697142784 |
|---|---|
| author | Ramane, Harishchandra S. Parvathalu, B. Patil, Daneshwari Ashoka, K. |
| author_facet | Ramane, Harishchandra S. Parvathalu, B. Patil, Daneshwari Ashoka, K. |
| contents | The graphs with all equal negative or positive eigenvalues are special kind in the spectral graph theory. In this article, several iterated line graphs $\mathcal{L}^k(G)$ with all equal negative eigenvalues $-2$ are characterized for $k\ge 1$ and their energy consequences are presented. Also, the spectra and the energy of complement of these graphs are obtained, interestingly they have exactly two positive eigenvalues with different multiplicities. Moreover, we characterize a large class of equienergetic graphs which generalize some of the existing results. There are two different quotient matrices defined for an equitable partition of $H$-join (generalized composition) of regular graphs to find the spectrum (partial) of adjacency matrix, Laplacian matrix and signless Laplacian matrix, it has been proved that these two quotient matrices give the same respective spectrum of graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_02276 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Iterated line graphs with only negative eigenvalues $-2$, their complements and energy Ramane, Harishchandra S. Parvathalu, B. Patil, Daneshwari Ashoka, K. Combinatorics 05C50, 05C76, 05C12 The graphs with all equal negative or positive eigenvalues are special kind in the spectral graph theory. In this article, several iterated line graphs $\mathcal{L}^k(G)$ with all equal negative eigenvalues $-2$ are characterized for $k\ge 1$ and their energy consequences are presented. Also, the spectra and the energy of complement of these graphs are obtained, interestingly they have exactly two positive eigenvalues with different multiplicities. Moreover, we characterize a large class of equienergetic graphs which generalize some of the existing results. There are two different quotient matrices defined for an equitable partition of $H$-join (generalized composition) of regular graphs to find the spectrum (partial) of adjacency matrix, Laplacian matrix and signless Laplacian matrix, it has been proved that these two quotient matrices give the same respective spectrum of graphs. |
| title | Iterated line graphs with only negative eigenvalues $-2$, their complements and energy |
| topic | Combinatorics 05C50, 05C76, 05C12 |
| url | https://arxiv.org/abs/2205.02276 |