Spectral Gap of the Largest Eigenvalue of the Normalized Graph Laplacian

Abstract We offer a new method for proving that the maxima eigenvalue of normalized graph Laplacian with n vertices is at least $$\frac{n+1}{n-1}$$ n + 1 - provided not complete and equality attained if only complement single edge or bipartite both parts size $$\frac{n-1}{2}$$ 2 . With same method, we also prove lower bound to largest in terms minimum vertex degree, this most