Algebraic Structures and Their ApplicationsAlgebraic Structures and Their Applications
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Feed provided by Algebraic Structures and Their Applications. Click to visit.Small graphs with exactly two non-negative eigenvalues
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Let $G$ be a graph with eigenvalues $lambda_1(G)geqcdotsgeqlambda_n(G)$. 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 $nleq12$ 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 $nleq12$ 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.Sat, 30 Sep 2017 20:30:00 +0100