From Graphs to Reactions: Unveiling the Oxidizing Power of KMnO₄ and K₂Cr₂O₇ Using Innovative Graphical Tools

Abstract

This study uses graph theory to compare the oxidizing strengths of potassium permanganate (KMnOâ‚„) and potassium dichromate (Kâ‚‚Crâ‚‚O₇). Laplacian matrices for each compound were constructed to analyse their molecular structures. Topological indices indicate KMnOâ‚„ has a Wiener index of 16 and Zagreb indices of 80 and 128, whereas Kâ‚‚Crâ‚‚O₇ shows higher values (88, 94, and 132), suggesting a more complex structure. Eigenvalue analysis reveals KMnOâ‚„’s spectral radius is 10 compared to 7.85 of  Kâ‚‚Crâ‚‚O₇, implying Kâ‚‚Crâ‚‚O₇ has a higher potential for electron transfer. The characteristic polynomials of the Laplacian matrices emphasizing structural variations. These results support with experimental interpretation, confirming KMnOâ‚„’s higher oxidizing power and indicating the use of graph theory in chemical analysis it was proved by regression analysis and gives the profound significance of relative directionality as higher stability.