@article{Gao2025, 
author = {Hui Gao},
title = {Extremal graphs with maximum complementary second Zagreb index},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {7},
pages = {16105-16116},
keywords = {complementary second Zagreb index, extremal graph, mixed graph, orientation, cM2-maximal},
url = {https://www.sciopen.com/article/10.3934/math.2025721},
doi = {10.3934/math.2025721},
abstract = {The complementary second Zagreb index of a graph    G is defined as    c      M          2        (  G  )  =      ∑          u      v      ∈      E      (      G      )            |        d          G        (  u      )          2        −      d          G        (  v      )          2            |  . In this paper, we prove that a graph having maximum complementary second Zagreb index among all graphs of order    n is isomorphic to        K          m        ∨            K              n        −        m              ¯   for some    1  ≤  m  <  ⌈      n    2    ⌉, confirming a conjecture of Furtula and Oz.}
}