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First Zagreb Index


The first Zagreb index for a graph with vertex count n and vertex degrees d_i for i=1, ..., n is defined by

 Z_1=sum_(i=1)^nd_i^2.

The notations Z_1 (e.g., Lin et al. 2023) and M_1 (e.g., Devillers and Balaban 2000) are variously used.

The first Zagreb matrix is related to earlier indices F (defined by Platt) and N_2 (defined by Gordon and Scantlebury) by

 F=2N_2=Z_1-m,

where m is the edge count of a graph G (Devillers and Balaban p. 27, 2000).


See also

Second Zagreb Index, Zagreb Indices

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References

Alikhani, S. and Ghanbari, N. "Golden Ratio in Graph Theory: A Survey." 9 Jul 2024. https://arxiv.org/abs/2407.15860.Devillers, J. and Balaban, A. T. (Eds.). "The Zabgreb Indices." In Topological Indices and Related Descriptors in QSAR and QSPR. Amsterdam, Netherlands: Gordon and Breach, pp. 28-29, 2000.Gutman, I.; Ruščić, B.; Trinajstić, N.; and Wilcox, C. F. "Graph Theory and Molecular Orbitals. XII. Acyclic Polyenes." J. Chem. Phys. 62, 3399-3409, 1975.Lin, Z.; Wang, J.; and Cai, M. "The Laplacian Spectral Ratio of Connected Graphs." 21 Feb 2023. https://arxiv.org/abs/2302.10491v1.

Cite this as:

Weisstein, Eric W. "First Zagreb Index." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FirstZagrebIndex.html

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