The ABC (atom-bond connectivity) matrix weighted
adjacency matrix with weight
(1)
where vertex
degrees of the graph. In other words,
(2)
(Zheng et al. 2022).
It was introduced by Estrada et al. (2017) to model the enthalpy of formation
of alkanes (Zheng et al. 2023).
Its largest eigenvalue ABC
spectral radius , half the sum of its matrix elements is the ABC
index , and the sum of absolute values of its eigenvalues
is the ABC energy .
See also ABC Energy ,
ABC Index ,
ABC Spectral Radius ,
Adjacency
Matrix ,
Graph Matrix ,
Weighted
Adjacency Matrix
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References Estrada, E. "The ABC Matrix." J. Math. Chem. 55 , 1021-1033, 2017. Zheng, R.; Su, P.; and Jin. S. "Arithmetic-Geometric
Matrix of Graphs and Its Applications." Appl. Math. Comput. 42 ,
127764, 1-11, 2023. Referenced on Wolfram|Alpha ABC Matrix
Cite this as:
Weisstein, Eric W. "ABC Matrix." From
MathWorld https://mathworld.wolfram.com/ABCMatrix.html
Subject classifications
of a simple graph is a weighted
adjacency matrix with weight
are the vertex
degrees of the graph. In other words,
![[A_(ABC)]_(ij)={sqrt((d_i+d_j-2)/(d_id_j)) for i,j adjacent; 0 otherwise](/images/equations/ABCMatrix/NumberedEquation2.svg)
is called the ABC
spectral radius, half the sum of its matrix elements is the ABC
index, and the sum of absolute values of its eigenvalues
is the ABC energy.
