Further Results on the Quadratic Embedding Constants of Corona Graphs
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| Format: | Preprint |
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2026
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| author | Ferdi Baskoro, Edy Tri Santika, Aditya Purwa |
| author_facet | Ferdi Baskoro, Edy Tri Santika, Aditya Purwa |
| contents | The quadratic embedding constant (QEC) is a numerical invariant associated with quadratic embeddings of graphs into Hilbert spaces, and it is characterized in terms of the distance matrix. For corona graphs $G\odot H$, a general expression for $\mathrm{QEC}(G\odot H)$ can be described using $\mathrm{QEC}(G)$ together with spectral properties of $H$. However, this expression involves an additional spectral contribution determined by the adjacency matrix of $H$. In this paper, we analyze this contribution and provide an explicit description of the associated set $Γ$, allowing us to determine the quantity $γ= \max Γ$ that appears in the general formula for $\mathrm{QEC}(G\odot H)$. As applications, we compute the quadratic embedding constants for corona graphs of the form $G\odot H$ where $H$ is a regular graph. Finally, we provide conditions on $G$ and $H$ under which the quadratic embedding constant of $G\odot H$ coincides with the second largest eigenvalue of the distance matrix. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_14962 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Further Results on the Quadratic Embedding Constants of Corona Graphs Ferdi Baskoro, Edy Tri Santika, Aditya Purwa Combinatorics primary:05C50. secondary:05C12, 05C76, 15A63 The quadratic embedding constant (QEC) is a numerical invariant associated with quadratic embeddings of graphs into Hilbert spaces, and it is characterized in terms of the distance matrix. For corona graphs $G\odot H$, a general expression for $\mathrm{QEC}(G\odot H)$ can be described using $\mathrm{QEC}(G)$ together with spectral properties of $H$. However, this expression involves an additional spectral contribution determined by the adjacency matrix of $H$. In this paper, we analyze this contribution and provide an explicit description of the associated set $Γ$, allowing us to determine the quantity $γ= \max Γ$ that appears in the general formula for $\mathrm{QEC}(G\odot H)$. As applications, we compute the quadratic embedding constants for corona graphs of the form $G\odot H$ where $H$ is a regular graph. Finally, we provide conditions on $G$ and $H$ under which the quadratic embedding constant of $G\odot H$ coincides with the second largest eigenvalue of the distance matrix. |
| title | Further Results on the Quadratic Embedding Constants of Corona Graphs |
| topic | Combinatorics primary:05C50. secondary:05C12, 05C76, 15A63 |
| url | https://arxiv.org/abs/2603.14962 |