The second Zagreb index for a graph with vertex count 
and vertex
degrees 
for 
,
..., 
is defined by
 |
where 
is the edge set of 
.
Second Zagreb Index
See also
First Zagreb Index, Zagreb IndicesExplore with Wolfram|Alpha
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. "Second Zagreb Index." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SecondZagrebIndex.html