Quadratic Embedding Constants of Corona Graphs
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909970756272128 |
|---|---|
| author | Ferdi Baskoro, Edy Tri Obata, Nobuaki Santika, Aditya Purwa |
| author_facet | Ferdi Baskoro, Edy Tri Obata, Nobuaki Santika, Aditya Purwa |
| contents | The quadratic embedding constant (QEC) of a connected graph is defined to be the maximum of the quadratic function associated with its distance matrix on a certain unit sphere of codimension two. In this paper we derive a formula for the QEC of a corona graph $G\odot H$. It is shown that $\mathrm{QEC}(G\odot H)=ψ_{H*}^{-1}(\mathrm{QEC}(G))$ holds under some spectral assumptions on $H$, where $ψ_{H*}^{-1}$ is the inverse function of the most right branch of the analytic function $ψ_H$ defined by means of the main eigenvalues of the adjacency matrix of $H$. Moreover, if $H$ is a regular graph of which the adjacency matrix has the smallest eigenvalue $-2$, then the formula is written down explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17258 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quadratic Embedding Constants of Corona Graphs Ferdi Baskoro, Edy Tri Obata, Nobuaki Santika, Aditya Purwa Combinatorics 05C50, 05C12, 05C76, 15A63, 51K05 The quadratic embedding constant (QEC) of a connected graph is defined to be the maximum of the quadratic function associated with its distance matrix on a certain unit sphere of codimension two. In this paper we derive a formula for the QEC of a corona graph $G\odot H$. It is shown that $\mathrm{QEC}(G\odot H)=ψ_{H*}^{-1}(\mathrm{QEC}(G))$ holds under some spectral assumptions on $H$, where $ψ_{H*}^{-1}$ is the inverse function of the most right branch of the analytic function $ψ_H$ defined by means of the main eigenvalues of the adjacency matrix of $H$. Moreover, if $H$ is a regular graph of which the adjacency matrix has the smallest eigenvalue $-2$, then the formula is written down explicitly. |
| title | Quadratic Embedding Constants of Corona Graphs |
| topic | Combinatorics 05C50, 05C12, 05C76, 15A63, 51K05 |
| url | https://arxiv.org/abs/2512.17258 |