@article{He2023, 
author = {Shengjie He and Qiaozhi Geng and Rong-Xia Hao},
title = {The extremal unicyclic graphs with given diameter and minimum edge revised Szeged index},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {11},
pages = {26301-26327},
keywords = {unicyclic graph, diameter, edge revised Szeged index, edge Szeged index},
url = {https://www.sciopen.com/article/10.3934/math.20231342},
doi = {10.3934/math.20231342},
abstract = {Let    H be a connected graph. The edge revised Szeged index of    H is defined as    S      z          e              ∗        (  H  )  =      ∑          e      =      u      v      ∈              E        H              (      m          u        (  e      |    H  )  +                    m                  0                    (      e              |            H      )        2    )  (      m          v        (  e      |    H  )  +                    m                  0                    (      e              |            H      )        2    ), where        m          u        (  e      |    H  ) (resp.,        m          v        (  e      |    H  )) is the number of edges whose distance to vertex    u (resp.,    v) is smaller than to vertex    v (resp.,    u), and        m          0        (  e      |    H  ) is the number of edges equidistant from    u and    v. In this paper, the extremal unicyclic graphs with given diameter and minimum edge revised Szeged index are characterized.}
}