A fractional matching of a graph G is a function f: E(G)→[0,1] such that for each vertex v, ∑eϵΓG(v)f(e)≤1.. The fractional matching number of G is the maximum value of ∑e∈E(G)f(e) over all fractional matchings ...A fractional matching of a graph G is a function f: E(G)→[0,1] such that for each vertex v, ∑eϵΓG(v)f(e)≤1.. The fractional matching number of G is the maximum value of ∑e∈E(G)f(e) over all fractional matchings f. Tian et al. (Linear Algebra Appl 506:579–587, 2016) determined the extremal graphs with minimum distance Laplacian spectral radius among n-vertex graphs with given matching number. However, a natural problem is left open: among all n-vertex graphs with given fractional matching number, how about the lower bound of their distance Laplacian spectral radii and which graphs minimize the distance Laplacian spectral radii? In this paper, we solve these problems completely.展开更多
基金This work is supported by the Science and Technology Program of Guangzhou,China(No.202002030183)the Guangdong Province Natural Science Foundation(No.2021A1515012045)the Qinghai Province Natural Science Foundation(No.2020-ZJ-924).
文摘A fractional matching of a graph G is a function f: E(G)→[0,1] such that for each vertex v, ∑eϵΓG(v)f(e)≤1.. The fractional matching number of G is the maximum value of ∑e∈E(G)f(e) over all fractional matchings f. Tian et al. (Linear Algebra Appl 506:579–587, 2016) determined the extremal graphs with minimum distance Laplacian spectral radius among n-vertex graphs with given matching number. However, a natural problem is left open: among all n-vertex graphs with given fractional matching number, how about the lower bound of their distance Laplacian spectral radii and which graphs minimize the distance Laplacian spectral radii? In this paper, we solve these problems completely.
