@article{Yang2025, 
author = {Yang Yang and Yanyan Song and Haifeng Fan and Haiyan Qiao},
title = {A note on the generalized Gaussian Estrada index and Gaussian subgraph centrality of graphs},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {2},
pages = {2279-2294},
keywords = {generalized Gaussian Estrada index, generalized Gaussian subgraph centrality, statistical mechanics, adjacency matrix, equitable partition},
url = {https://www.sciopen.com/article/10.3934/math.2025106},
doi = {10.3934/math.2025106},
abstract = {Let    H be a simple, undirected, connected graph represented by its adjacency matrix        A  . For a vertex    u  ∈  V  (  H  ), the generalized Gaussian subgraph centrality of    u in    H is    G  S  C  (  u  ,  β  )  =  exp  ⁡            (              −        β                              A                    2                    )              u      u      , where    β  >  0 is the real number and represents the temperature. Furthermore, the generalized Gaussian Estrada index of    H is    G  E  E  (  H  ,  β  )  =      ∑          i      =      1        n    exp  ⁡      (          −      β              μ        i        2              )    =      ∑          u      =      1        n    G  S  C  (  u  ,  β  ), where        μ    1    ,      μ    2    ,  …  ,      μ    n   are the eigenvalues of        A   and    β  >  0. This study presents new computational formulas for the    G  S  C  (  u  ,  β  ) of graphs by employing an equitable partition and the star sets technique. We also investigated the influence of the parameter    β on the robustness of the formula through experiments. Additionally, we established some bounds for    G  E  E  (  H  ,  β  ).}
}