Establishes bounds on the Sombor index based on graph energy and matching properties, suggesting important implications for graph theory.
The Sombor index of the graph G is a degree based topological index, defined as SO = Sigma(uv is an element of E(G)) root d(u)(2) + d(v)(2) where d(u) is the degree of the vertex u, and E(G) is the edge set of G. Bounds on SO are established in terms of graph energy, size of minimum vertex cover, matching number, and induced matching number.
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Gutman et al. (2022) studied this question.
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