ON EXTREME ENTRIES OF PRINCIPAL EIGENVECTOR OF A GRAPH
B. Buzarbarua and P. Das
Let $G=(V,E)$ be a simple, connected graph. In this paper, we present some lower bound for the maximal entry of the principal eigenvector corresponding to the spectral radius $\lambda_1$ of $G$. Also, we find some lower bound for the ratio of the maximal entry to the minimal entry of the principal eigenvector. Moreover, we present some examples where our lower bounds are better than the bounds given by Cioaba and Gregory , Nikiforov  and Zhang .
Keywords: Spectral radius, Principal eigenvector, Non-regular graph, Complete multipartite graph.