ABSTRACT
A fractional matching of a graph G is a function f giving each edge a number in so that
for each
, where
is the set of edges incident to v. The fractional matching number of G, written
, is the maximum of
over all fractional matchings. In this paper, we study the connections between the fractional matching number and the Laplacian spectral radius of a graph. We also give some sufficient spectral conditions for the existence of a fractional perfect matching.
AMS CLASSIFICATION:
Acknowledgments
The authors would like to thank the anonymous referees very much for valuable suggestions and corrections which lead to a great improvement in the original paper.
Disclosure statement
No potential conflict of interest was reported by the authors.