@article{Mei2024, 
author = {Yinzhen Mei and Chengxiao Guo},
title = {The minimal degree Kirchhoff index of bicyclic graphs},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {7},
pages = {19822-19842},
keywords = {bicyclic graph, degree Kirchhoff index, resistance distance, Θ-graph},
url = {https://www.sciopen.com/article/10.3934/math.2024968},
doi = {10.3934/math.2024968},
abstract = {The degree Kirchhoff index of graph    G is defined as    K      f          ∗        (  G  )  =      ∑                  u        ,        v            ⊆      V      (      G      )        d  (  u  )  d  (  v  )      r          G        (  u  ,  v  ), where    d  (  u  ) is the degree of vertex    u and        r          G        (  u  ,  v  ) is the resistance distance between the vertices    u and    v. In this paper, we characterize bicyclic graphs with exactly two cycles having the minimum degree Kirchhoff index of order    n  ≥  5. Moreover, we obtain the minimum degree Kirchhoff index on bicyclic graphs of order    n  ≥  4 with exactly three cycles, and all bicyclic graphs of order    n  ≥  4 where the minimum degree Kirchhoff index has been obtained.}
}