@article{Altassan2023, 
author = {Alaa Altassan and Muhammad Imran and Bilal Ahmad Rather},
title = {On    A  B  C energy and its application to anticancer drugs},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {9},
pages = {21668-21682},
keywords = {adjacency matrix, ABC matrix, atom-bond connectivity, equienergetic graphs, correlation},
url = {https://www.sciopen.com/article/10.3934/math.20231105},
doi = {10.3934/math.20231105},
abstract = {For a simple connected graph    Γ with node set    V  (  Γ  )  =  {      w          1        ,      w          2        ,  …  ,      w          n        } and degree sequence        d          i      , the atom-bond connectivity (   A  B  C) matrix of    Γ has an    (  i  j  )-th entry                                d                      i                          +                  d                      j                          −        2                              d                      i                                    d                      j                               if        w          i       is adjacent to        w          j       and    0, otherwise. The multiset of all eigenvalues of    A  B  C matrix is known as the    A  B  C spectrum and their absolute sum is known as the    A  B  C energy of    Γ  . Two graphs of same order are known as    A  B  C equienergetic if they have the same    A  B  C energy but share different    A  B  C spectrum. We describe the    A  B  C spectrum of some special graph operations and as an application, we construct the    A  B  C equienergetic graphs. Further, we give linear regression analysis of    A  B  C index/energy with the physical properties of anticancer drugs. We observe that they are better correlated with    A  B  C-energy.}
}