[2209.05694] the spectrum of the complement of the graph with the given connectivity

This paper was retracted by Wang Taira

Download the PDF of the paper by Huan Qiu and two other authors titled “Spectrum of Spectra of Complements of Graphs with Specified Connectivity”.

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overview: The spectral radius of graph $G$ is the largest eigenvalue of the adjacency matrix of $G$. The smallest eigenvalue of graph $G$ is the smallest eigenvalue of the adjacency matrix of $G$. In this paper, we determine the graph that achieves the smallest spectral radius and smallest eigenvalue, respectively, among all complements of connected simple graphs with given connectivity. The spectral radius of graph $G$ is the largest eigenvalue of the adjacency matrix of $G$. The smallest eigenvalue of graph $G$ is the smallest eigenvalue of the adjacency matrix of $G$. In this paper, we determine the graph that achieves the smallest spectral radius and smallest eigenvalue, respectively, among all complements of connected simple graphs with given connectivity.