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 (KMnO₄) and potassium dichromate (K₂Cr₂O₇). Laplacian matrices for each compound were constructed to analyse their molecular structures. Topological indices indicate KMnO₄ has a Wiener index of 16 and Zagreb indices of 80 and 128, whereas K₂Cr₂O₇ shows higher values (88, 94, and 132), suggesting a more complex structure. Eigenvalue analysis reveals KMnO₄’s spectral radius is 10 compared to 7.85 of  K₂Cr₂O₇, implying K₂Cr₂O₇ has a higher potential for electron transfer. The characteristic polynomials of the Laplacian matrices emphasizing structural variations. These results support with experimental interpretation, confirming KMnO₄’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.