Spectral radius and fractional matchings in graphs

Abstract

A fractional matching of a graph G is a function f giving each edge a number in [0,1] so that e∈Γ(v) f (e) ≤ 1 for each

On the Size, Spectral Radius, Distance Spectral Radius and Fractional Matchings in Graphs

“…For example, for an r -regular graph G by setting each edge weight to , but not every r -regular graph has a perfect matching. In 2016, O [10] determined the connection between the spectral radius and fractional matching number among connected graphs with given minimum degree.…”

“…Motivated by [10–12], it is natural and interesting to give some sufficient conditions to ensure that a graph contains a fractional perfect matching. Here, we focus on sufficient conditions including a structure graph condition, adjacency spectral graph condition and distance spectral graph condition.…”