Local Turán inequalities for walks and the spectral radius

Feng Liu, Shuang Sun, Yan Wang +1

Nikiforov's well-known spectral Turán inequality for walks states that, for every graph $G$ with clique number $\ddot{I}‰(G)$, $\hat{I}{»}^r(G)\le w_r(G)(1-1/\ddot{I}‰(G))$, where $\hat{I}»(G)$ is the larges…