Spectrum and Local Metric Dimension of Andr\'asfai Graphs

Abstract

The Andr\'asfai graph $And(k)$ for $k\geq 1$ is a circulant and triangle-free graph on 3k-1 vertices. In this paper, we have determined the least eigenvalue, second largest eigenvalue, and the number of distinct eigenvalues of the adjacency spectrum of $And(k)$. Also, we have found out the local metric dimension of $And(k)$