The ABC (atom-bond connectivity) matrix of a simple graph is a weighted
adjacency matrix with weight

(1)

where are the 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 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 .

See also ABC Energy ,

ABC Index ,

ABC Spectral Radius ,

Adjacency
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.
Cite this as:
Weisstein, Eric W. "ABC Matrix." From
MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/ABCMatrix.html

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