Author/Authors :
Derikvand, Tajedin Department of Mathematics - Marvdasht Branch, Islamic Azad University, Marvdasht, Iran , Oboudi, Mohammad Reza Department of Mathematics - College of Sciences, Shiraz University, Shiraz, Iran
Abstract :
Let G be a graph with eigenvalues λ1(G)≥⋯≥λn(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≤12 and λ1(G)≥0, λ2(G)≥0 and λ3(G)<0. We obtain that there are exactly 1575 connected graphs G on n≤12 vertices with λ1(G)>0, λ2(G)>0 and λ3(G)<0. We find that among these 1575 graphs there are just two integral graphs.
