关于可加加权Harary指标的极单圈图
Extremal unicyclic graphs with respect to additively weighted Harary index
摘要：
本文定义圈星图CSk，n-k为n个顶点的图，由长度为k的圈和附加在该圈的同一个顶点上的n-k个叶组成。我们还定义了圈路图CPk，n-k是由长度为k的圈和n-k个顶点上的路组成的n个顶点上的图，其中路的一端与圈上的一个顶点相连。我们证明了圈星图CS3，n-3是n阶单圈图中唯一的关于加权Harary指数的极大图，而圈路图CP 3，n-3是唯一的极小单圈图（这里n必须至少为5）.给出了极单圈图的加权Harary指数的值，从而给出了n阶单圈图的加权Harary指数的上界和下界.
英文摘要：
In this paper we define cycle-star graph CSk,n-k to be a graph on n vertices consisting of the cycle of length k and n-k leafs appended to the same vertex of the cycle. Also, we define cycle-path graph CPk,n-k to be a graph on n vertices consisting of the cycle of length k and of path on n-k vertices whose one end is linked to a vertex on a cycle. We establish that cycle-star graph CS3,n-3 is the only maximal graph with respect to additively weighted Harary index among all unicyclic graphs on n vertices, while cycle-path graph CP3,n-3 is the only minimal unicyclic graph (here n must be at least 5). The values of additively weighted Harary index for extremal unicyclic graphs are established, so these values are the upper and the lower bound for the value of additively weighted Harary index on the class of unicyclic graphs on n vertices.
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