Small graphs with exactly two non-negative eigenvalues

Authors

  • Mohammad Reza Oboudi Department of Mathematics, College of Sciences, Shiraz University, Shiraz, 71457-44776, Iran
  • Tajedin Derikvand Department of Mathematics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
Abstract:

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 $lambda_3(G)0$, $lambda_2(G)>0$ and $lambda_3(G)

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Journal title

volume 4  issue 1

pages  1- 18

publication date 2017-10-01

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