On the Reduced Sombor Index and Its Applications

Based on elementary geometry, a novel vertex-degree-based molecular structure descriptor was recently introduced by Gutman in the chemical graph theory, defined as SOred(G) = Sigma(uv is an element of E(G)) root(d(u) - 1)(2) + (d(v) - 1)(2), where d(u) denotes the degree of vertex u in G, and named as reduced Sombor index. It was demonstrated that the reduced Sombor index can help to exert modest discriminative potential and predict physico-chemical properties of molecules, and it performs with slightly better predictive potential than the Sombor index [10,27]. Based on the results of testing predictive potential of reduced Sombor indices, it may be successfully applied on modeling thermodynamic properties of compounds [27]. In this paper, we obtain some bounds for reduced Sombor index of graphs with given several parameters (such as maximum degree Delta, minimum degree delta, matching number beta, chromatic number chi, independence number alpha, clique number omega), some special graphs (such as unicyclic grahs, bipartite graphs, graphs with no triangles, graphs with no Kr+1 (2 <= r <= n - 1) and the Nordhaus-Gaddum-type results. We also characterize some extremal molecular graphs. Then we obtain the expected values of reduced Sombor index in random polyphenyl chains. At last, we apply the reduced Sombor index to graph spectrum and energy problems.