Spectral radius and fractional matchings in graphs

Suil O

A {\it fractional matching} of a graph $G$ is a function $f$ giving each edge a number in $[0,1]$ so that ${\sum }_{e\in \Gamma (v)}f(e)\le 1$ for each $v\in V(G)$, where $\Gamma (v)$ is the s…