Exploring Graphs with Distinct $M$-Eigenvalues: Product Operation, Wronskian Vertices, and Controllability

Haiying Shan, Xiaoqi Liu

Let ${\mathcal{G}}^M$ denote the set of connected graphs with distinct $M$-eigenvalues. This paper explores the $M$-spectrum and eigenvectors of a new product $G{\circ }_{C}H$ of graphs…