4 problems

All graphs considered are finite, undirected and simple. A graph is co-edge-regular with parameters $(n,k,c)$ if it is $k$-regular on $n$ vertices and every two distinct non-adjace…

Let $G$ be a connected $k$-regular graph with $n$ vertices and co-edge-regular with parameter $\mu$, having four distinct eigenvalues. Let $t\geq 2$ be an integer. Tan et al.'s con…

Let $\Gamma$ be a connected co-edge-regular graph with parameters $(n,k,\mu)$ and four distinct eigenvalues. For an integer $t\geq 2$, let $\theta_{\min}(\Gamma)$ denote its smalle…

Let $\Gamma$ be a connected co-edge-regular graph with four distinct eigenvalues. Let $t\geq 2$ be an integer and write $|V(\Gamma)|=n(\Gamma)$. An $s$-clique extension is a graph…