Energy and spectral radius of Zagreb matrix of graph with applications
https://doi.org/10.17586/2220-8054-2024-15-3-315-324
Abstract
The Z-matrix of a simple graph Γ is a square symmetric matrix, whose rows and columns correspond to the vertices of the graph and the ijth entry is equal to the sum of the degrees of ith and jth vertex, if the corresponding vertices are adjacent in Γ, and zero otherwise. The Zagreb eigenvalues of Γ are the eigenvalues of its Z-matrix and the Zagreb energy of Γ is the sum of absolute values of its Zagreb eigenvalues. We study the change in Zagreb energy of a graph when the edges of the graph are deleted or rotated. Suppose Γ is a graph obtained by identifying u ∈ V(Γ1) and v ∈ V(Γ2) or adding an edge between u and v, then it is important to study the relation between Zagreb energies of Γ1, Γ2 and Γ. The highlight of the paper is that, the acentric factor of n-alkanes appear to have a strong positive correlation (where the correlation coefficient is 0.9989) with energy of the Z-matrix. Also, the novel correlation of the density and refractive index of n-alkanes with spectral radius of the Z-matrix has been observed.
About the Authors
Sh. S. Shetty
http://nanojournal.ifmo.ru
Manipal Academy of Higher Education
India
Manipal Academy of Higher Education
India
Shashwath S. Shetty
Manipal Institute of Technology; Department of Mathematics
576104; Karnataka; Manipal
K. A. Bhat
http://nanojournal.ifmo.ru
Manipal Academy of Higher Education
India
Manipal Academy of Higher Education
India
K. Arathi Bhat
Manipal Institute of Technology; Department of Mathematics
576104; Karnataka; Manipal
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Review
For citations:
Shetty Sh.S., Bhat K.A. Energy and spectral radius of Zagreb matrix of graph with applications. Nanosystems: Physics, Chemistry, Mathematics. 2024;15(3):315-324. https://doi.org/10.17586/2220-8054-2024-15-3-315-324
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