Eigenvalue-free interval for Seidel matrices of cographs |
Received:April 10, 2024 Revised:June 13, 2024 |
Key Words:
cograph Seidel matrix eigenvalue-free interval
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Fund Project:National Natural Science Foundation of China (Grant No. 12001006) and Natural Science Foundation of Universities of Anhui (Grant No. 2023AH050904) |
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Abstract: |
The distribution of Seidel eigenvalues of cographs is investigated in this paper. We prove that there is no Seidel eigenvalue of cographs in the interval
$(-1, 1)$. We also show the optimality of the interval $(-1,1)$ in the sense that for any $\epsilon>0$ either of the intervals $(1,1+\epsilon)$ and $(-1-\epsilon,-1)$ contains a Seidel eigenvalue of some cograph of order $n$ when $n$ is sufficiently large. |
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