The Largest and Smallest Eigenvalues of Matrices and Some Hamiltonian Properties of Graphs

Rao Li

Let $G=(V,E)$ be a graph. We define matrices $M(G;\hat{I}\pm ,{\hat{I}}^2)$as $\hat{I}\pm D+{\hat{I}}^{2}A$, where $\hat{I}\pm$, ${\hat{I}}^2$ are real numbers such that $(\hat{I}\pm ,{\hat{I}}^2)\ne (0,0)$ and $D$ and $A$ are the diagonal ma…