TEMO theorem for Sombor index

Source abstract

TEMO = topological effect on molecular orbitals was discovered by Polansky and Zander in 1982, in connection with the eigenvalues of molecular graphs. Eventually, analogous regularities were established for a variety of other topological indices. We now show that a TEMO-type regularity also holds for the Sombor index ($SO$): For the graphs $S$ and $T$, constructed by connecting a pair of vertex-disjoint graphs by two edges, $SO(S) < SO(T)$ holds. Analogous relations are verified for several other degree-based graph invariants.