Eccentricity spectral properties of $\mathcal{C}$-graphs
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914049088815104 |
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| author | Ashokan, Anjitha A V, Chithra |
| author_facet | Ashokan, Anjitha A V, Chithra |
| contents | A cograph is a simple graph that contains no induced path on four vertices. In this paper, we consider $\mathcal{C}$-graphs, which are a specific class of cographs, defined as $$\overline{\overline{\overline{K_{α_{1}}}\cup K_{α_{2}}}\cup \cdots \cup K_{α_{2k}}},$$ %\text{ where } k \geq 2, α_{2k}\geq 2,$$
where $k \geq 2$, $α_{2k} \geq 2$, and $K_{α_{i}}$ denotes the complete graph on $α_{i}$ vertices. We investigate the spectral properties of the eccentricity matrix of this particular class of cographs. Additionally, we determine the irreducibility and inertia of the eccentricity matrix of $\mathcal{C}$-graphs. Furthermore, we identify an interval $(-1-\sqrt{2},-2)\cup (-2,0)$ in which these graphs have no eccentricity eigenvalues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16657 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Eccentricity spectral properties of $\mathcal{C}$-graphs Ashokan, Anjitha A V, Chithra Combinatorics 05C50, 05C76 A cograph is a simple graph that contains no induced path on four vertices. In this paper, we consider $\mathcal{C}$-graphs, which are a specific class of cographs, defined as $$\overline{\overline{\overline{K_{α_{1}}}\cup K_{α_{2}}}\cup \cdots \cup K_{α_{2k}}},$$ %\text{ where } k \geq 2, α_{2k}\geq 2,$$ where $k \geq 2$, $α_{2k} \geq 2$, and $K_{α_{i}}$ denotes the complete graph on $α_{i}$ vertices. We investigate the spectral properties of the eccentricity matrix of this particular class of cographs. Additionally, we determine the irreducibility and inertia of the eccentricity matrix of $\mathcal{C}$-graphs. Furthermore, we identify an interval $(-1-\sqrt{2},-2)\cup (-2,0)$ in which these graphs have no eccentricity eigenvalues. |
| title | Eccentricity spectral properties of $\mathcal{C}$-graphs |
| topic | Combinatorics 05C50, 05C76 |
| url | https://arxiv.org/abs/2509.16657 |