一类单圈图的度基尔霍夫指数

The Degree Kirchhoff Index of a Class of Unicyclic Graphs

设G是简单连通图,顶点集为V(G).图G的度基尔霍夫指数定义为图G中所有顶点对的度与顶点之间的电阻距离乘积的和.棒棒糖图Ln,k是路Pn-k的一个端点连接到圈Ck的一个顶点得到的一类特殊的单圈图.给出首先给出Ln,k的度基尔霍夫指数计算公式,然后刻画了相应的极图.

Let G be a connected graph with vertex set V（G）. The degree Kirchhoff index of G is defined as the sum of products between degree of all pairs of vertices and their resistance distances. The lollipop graph Ln-k is a class of special unicyclic graphs which comes from joining an endpoint of Pn-k to one vertex of the cycle Ck. In this paper, the authors firstly give the formula for computing the degree Kirchhoff index of L,,k at first, and then characterize the extremal graphs with respect to degree Kirchhoff index in L~,k.