On the limit points of the smallest eigenvalues of regular graphs
In this paper, we give infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval and also infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval where alpha (1) is the smallest root of the polynomial x (3) + 2x (2) - 2x - 2. From these results, we determine the largest and second largest limit points of smallest eigenvalues of regular graphs less than -2. Moreover we determine the supremum of the smallest eigenvalue among all connected 3-regular graphs with smallest eigenvalue less than -2 and we give the unique graph with this supremum value as its smallest eigenvalue.
limit point smallest eigenvalue regular graph