A 1-planar graph G is called maximal, if the graph obtained from G by adding any new edge is not 1-planar. Clearly, a maximal 1-planar graph of order at least 3 is 2-connected. In this paper, we study the spectral radius of 1-planar graphs of given order. The rest of this ...
Minors play a key role in graph theory, and extremal problems on forbidding minors have attracted appreciable amount of interest in the past decades. In this paper, we focus on spectral extrema of Ks,t-minor free graphs, and determine extremal graphs with maximum spectral radius over all Ks,...
Through an analysis of eigenvalue mean, dispersion, and extrema statistics, we demonstrate the efficacy of these spectral techniques in characterizing critical points in both two and three dimensions. Crucially, we propose a significant modification to this spectral approach, which emerges as a ...