一类满足A(H)=3的新图族

One infinite class of new graphs with A(H)=3

图H中以半径为联系数的顶点称为H的中心点,全体中心点集的诱导子图称为H的中心。若图H中存在非中心点,称图H为非自中心图,且A(H)=n,n∈{2,3,4},已经知道对任意的树T,恒有A(T)≠3,首先给出了一个满足A(H)=3的图,进一步给出一类含有4n个一度顶点的满足A(H)=3的新图族。

In graph H, the vertex is the central vertex if its related number is the radius of H, the induced subgraph of the set of all central vertexes is the center of H. H is a non-self centered graph if there is a non-central vertex, and A(H)=n, n∈{2, 3, 4}. It is known that A(T)≠3 for all tree T. A new graph with A(H)= 3 is constructed and one infinite class of new graphs with A(H)= 3 and contains 4n vertices of degree one is provided.