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arXiv · 2212.07319

Spectral properties of $\mathcal{C}$-graphs

Santanu Mandal·Ranjit Mehatari
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Abstract

Assumed to be undirected, simple, and connected are all of the graphs in this study, and adjacency matrix $A$ serves as the associated matrix. In this paper we show that it is possible to relate a creation sequence for a type of cographs (we call it $\mathcal{C}$-graphs). Those cographs can be defined by a finite sequence of natural numbers. Using that sequence we obtain the inertia of the cograph under consideration. An extended eigenvalue-free set from $(-1,0)$ to $\big{[}\frac{-1-\sqrt{2}}{2}, -1)\cup (-1, 0) \cup (0, \frac{-1+\sqrt{2}}{2}\alpha_{min}\big{]}$, (where $\alpha_{min}\geq1$ is the smallest integer of the creation sequence) is obtained for the cographs under consideration. Additionally, an exact formula is found for the characteristic polynomial.

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Santanu Mandal, Ranjit Mehatari. 2022-12-14. Spectral properties of $\mathcal{C}$-graphs. https://arxiv.org/abs/2212.07319

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