Sombor index of directed graphs (2022)
Let be a digraph with set of arcs . The Sombor index of is defined as () = 1 2 ∑ ∈ √( + )2 + ( − )2 , where + and − are the out-degree and in-degree of the vertices and of . When is a graph, we recover the Sombor index of graphs, a molecular descriptor recently introduced with a good predictive potential and a great research activity this year. In this paper we initiate the study of the Sombor index of digraphs. Specifically, we find sharp upper and lower bounds for over the class of digraphs with non-isolated vertices, the classes and of connected and strongly connected digraphs on vertices, respectively, the class of oriented trees () with vertices, and the class () of orientations of a fixed graph .