朱忠熏,洪运朝,罗阿木,王维峰.具有乘积度-基尔霍夫指标极值的双圈图[J].中南民族大学学报自然科学版,2017,(2):148-154
具有乘积度-基尔霍夫指标极值的双圈图
Bicyclic Graphs with Extremal Multiplicative Degree-Kirchhoff Index
  
DOI:
中文关键词: 距离  乘积度-基尔霍夫指标  双圈图
英文关键词: distance  multiplicative degree-Kirchhoff index  bicyclic graphs
基金项目:国家自然科学基金资助项目 (61070197);中南民族大学中央高校基本科研业务费专项资金资助项目(CZQ10007)
作者单位
朱忠熏,洪运朝*,罗阿木,王维峰 中南民族大学 数学与统计学学院武汉 430074 
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中文摘要:
      对于一个图G,乘积度-基尔霍夫指标定义为R*(G)=∑dG(x)dG(y)rG(x,y).基于前人的一些研究成果,用类似于和的度-基尔霍夫指标应用在双圈图中的方法,把乘积度-基尔霍夫指标运用到双圈图中.首先给出了关于*(G)的一些图变换,然后根据这些图变换,确定了恰好有两个圈的n阶双圈图的最小和最大的乘积度-基尔霍夫指标的值及其对应的极值图.度-基尔霍夫指标广泛应用于电流网络、化学、马尔可夫链和欧氏距离等各个方面.
英文摘要:
      For a graph G, the multiplicative degree-Kirchhoff index is defined as R*(G)=∑dG(x)dG(y)rG(x,y). Based on the previous research results,similar to the additive degree-Kirchhoff index in the bicyclic graphs,the method of the same problem on the multiplicative degree-Kirchhoff index to the bicyclic graphs are discussed. First, some transformations on R*(G) are given,and then according to these transformations,the values of the minimum and maximum multiplicative degree-Kirchhoff index of bicyclic graphs with n-vertex having precisely two cycles are obtained and the corresponding extremal graphs are characterized. The degree-Kirchhoff index is widely used in the fields of electrical network,chemistry,Markov chain and Euclidean distance,and so on.
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