Extremal $ABS$ Spectral Radius in Bicyclic and Bipartite Unicyclic Graphs

Abstract

The ABS spectral radius of a graph G is defined as the largest eigenvalue of its $ABS$ matrix. Motivated by recent studies on this parameter, in this paper, we determine the bipartite unicyclic graphs that attain the largest $ABS$ spectral radius. Furthermore, we characterize the bicyclic graphs that attain the largest and the second largest $ABS$ spectral radii.