【摘要】 一个图G的乘积离心率电阻距离ξ*R(G)是在图上的所有无序顶点对的顶点对应的离心率和顶点对之间的电阻距离的乘积的和.本文运用了图变换的方法,分别刻画了所有的n个顶点的单圈图中,具有最大、第二大、最小和第二小乘积离心率电阻距离的极值图.进一步,分别刻画了所有的n个顶点且给定最大度的单圈图中,具有最大、第二大和第三大乘积离心率电阻距离的极值图.更多还原

【Abstract】 The multiplicative eccentricity resistance-distance ξ*R(G) of a graph G is the sum of the product the corresponding eccentricity of vertices and the resistance-distance between the pairs of vertices of all unordered pairs of vertices on the graph. In this paper, we use the transformation method to characterize the extremal graphs having the maximum, the second maximum, the minimum and the second minimum multiplicative eccentricity resistance-distance among n-vertex unicyclic graphs, respectively. Moreover,we characterize the extremal graphs having the maximum, the second maximum and the third maximum multiplicative eccentricity resistance-distance among n-vertex unicyclic graphs with given maximum degree ?, respectively.更多还原