Laplacian Coefcients Of Trees With Fxed Matching Number

Trees are undirected graphs without loops or multiple edges,the Laplacian poly-nomial is:∧（G,λ）=det（λIn-L）=Σkn=0（-l）kCkλn-k,Cn₂（T）is Wiener index of T.For two trees with n vertices,if（C0（T1）,…, Cn（T1））≤（C0（T2）,…, Cn（T2））,we callT2majorize T1,asT1≤T2.We already know that for fixed matching number,trees that minimize all Laplacian coefficients have been found,but trees that maximize all Laplacian coefficients have not been found.In this paper we will discuss when match-ing number is2,3,4,what kind of structure the trees with that maximize all Laplacian coefficients and majorize relationship.