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I would like to know what is valence molecular connectivity index of 3rd order cluster. Please provide an example?

Thanks for your help.

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It sounds like you're needing help with chemical graph theory.

I'm no expert in this topic, but it is one that has interested me in the past. Hence I can recommend 'Topological Methods in Chemistry' by R. E. Merrifield and H. E. Simmons—a book which explicitly deals with chemical graph theory in chapters 3 and 4; various topological indices feature throughout.

As a complement to this book, I would recommend the book on Topology by Munkres. The above book isn't rigorous enough to approach this topic perhaps, and so a mathematical treatise is also needed. I'm currently working through these topics myself for my own research.

It doesn't quite answer your question, but I hope it helps in your lofty quest!

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