The concept of Sombor index (SO) was recently introduced by Gutman in the chemical graph theory. It is a vertex-degree-based topological index and is denoted by Sombor index SO: SO=SO(G)=∑vivj∈E(G)dG(vi)2+dG(vj)2, where dG(vi) is the degree of vertex vi in G. Here, we present novel lower and upper bounds on the Sombor index of graphs by using some graph parameters. Moreover, we obtain several relations on Sombor index with the first and second Zagreb indices of graphs. Finally, we give some conclusions and propose future work.

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For a (molecular) graph G with vertex set

In general, the relations among Zagreb polynomials on three graph operators are discussed in this paper. Specifically, relations between Zagreb polynomials of a graph G and a graph obtained by applying the operators S(G), R(G) and Q(G) are investigated. In a separate section, the relation between Zagreb polynomial of a graph G and its corona is also described.