What is the use of finding indices of a graph?

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Sureshkumar Somayajula

Yes, we can compare these indices, but with important considerations:

Wiener index measures sum of distances between all pairs of vertices
First Zagreb index measures sum of squared degrees of vertices
They operate on different structural features, so their absolute values have different scales

Fabrice Clerot

it's been done for trees : Article Comparison between the Wiener index and the Zagreb indices a...

also for more very restricted classes of graphs

https://users.fmf.uni-lj.si/klavzar/preprints/match84n3_595-610.pdf