I apologise if this looks inappropriate. I tried to replicate the question here. However, I could not post any image and thus I would only post the link for a clear explanation of my problem. https://chemistry.stackexchange.com/questions/105146/finding-the-weighted-parameters-of-the-vertex-adjacency-matrix-for-a-derivative
2026-04-04 12:18:31.1775305111
Finding the weighted parameters of the vertex adjacency matrix for a derivative of azulene
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As I understood you question, you ask when in the adjacency matrix (VAM) of a weighted graph representing some molecule, we have to put $k$ and $h$. As I understood from the explanation at Chemistry.SE, we should do this when these values of $k$ and $h$ are shown at the molecule representation, like that at Fig.12. I think the following paragraph (“The parameters $h$ and $k$ depend,...”) explain the chemical conditions, when and which values of $k$ and $h$ have to be shown at the molecule representation. But I think the last question belongs to chemistry, not to mathematics.