فهرست نشریات علمی دسترسی آزاد ایران

Let $G$ be a graph with eigenvalues $\lambda_1(G)\geq\cdots\geq\lambda_n(G)$. In this paper we find all simple graphs $G$ such that $G$ has at most twelve vertices and $G$ has exactly two non-negative eigenvalues. In other words we find all graphs $G$ on $n$ vertices such that $n\leq12$ and $\lambda_1(G)\geq0$, $\lambda_2(G)\geq0$ and $\lambda_3(G)<0$. We obtain that there are exactly $1575$ connected graphs $G$ on $n\leq12$ vertices with $\lambda_1(G)>0$, $\lambda_2(G)>0$ and $\lambda_3(G)<0$. We find that among these $1575$ graphs there are just two integral graphs.