On the Zero Forcing Number and Spectral Radius of Graphs

Abstract

In this paper, we determine the graphs (respectively, trees) with maximum spectral radius among all graphs (respectively, trees) with zero forcing number at most $k$. As an application, we give a sharp lower bound for the zero forcing number of graphs involving the spectral radius.

Spectral bounds for the zero forcing number of a graph

“…Moreover, Zhang, Wang, Wang and Ji [13] determined the graphs (respectively, trees) with maximum spectral radius among all graphs (respectively, trees) with zero forcing number at most k. By their results they also provided a sharp lower bound for the zero forcing number of graphs involving its spectral radius.…”

Comparison of Contents Design in Mathematical Inquiry in High School Textbooks

“…Gould asked in [15] the following question: What spectral conditions imply a graph contains a chorded cycle? Zheng et al [29] answered Gould's question by showing that any graph G of order n 6 with ρ(G) ρ(K 2,n−2 ) contains a chorded cycle unless G ∼ = K 2,n−2 . Different answers are provided via the signless Laplacian spectral radius [24].…”