Explicit computation of minimum second neighborhood degree spectra and energies for commuting graphs of rings of orders p^2, p^3, p^4, p^5, p^2 q and p^3 q, establishing MSN-integrality without hyperintegrality and resolving two prior conjectures.
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Minimum second neighborhood degree energy of commuting graphs of finite rings
Explicit computation of minimum second neighborhood degree spectra and energies for commuting graphs of rings of orders p^2, p^3, p^4, p^5, p^2 q and p^3 q, establishing MSN-integrality without hyperintegrality and resolving two prior conjectures.