树T(1,6,n)及其补图的匹配唯一性

The Matching Uniqueness of T(1,6,n) and Its Complement

设μ(G,x)表示图G的匹配多项式.对每个图均有唯一的一个匹配多项式,但每一个匹配多项式所对应的图未必唯一.若μ(H,x)=μ(G,x),均有H G,则称图G是匹配唯一的.利用图的匹配多项式及最大实数根的性质证明了树T(1,6,n)及补图匹配唯一的充要条件是n≠6,9,17.

Let μ（G,x） be a matching polynomial of graph G.There must be only one matching polynomial for each graph,but the graph may not be unique for each matching polynomial.A graph G is said to have matching uniqueness if μ（H,x）=μ（G,x） as if implies that H is ismorphic to G.It is proved that T（1,6,n） and its complement can have matching uniqueness if and only if n≠6,9,17 and it is done by making use of the properties of graph＇s matching polynomial and its maximum real roots.