Sombor index of directed graphs

被引:1
作者
Cruz, Roberto [1 ]
Monsalve, Juan [1 ]
Rada, Juan [1 ]
机构
[1] Univ Antioquia, Inst Matemat, Medellin, Colombia
关键词
Sombor index; Digraphs; Connected digraphs; Strongly connected digraphs; Orientations; TOPOLOGICAL INDEXES;
D O I
10.1016/j.heliyon.2022.e09035
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
Let D be a digraph with set of arcs A. The Sombor index of D is defined as SO(D) = 1/2 sigma(uv is an element of A)root(d(u)(+))(2) + (d(v)(-))(2), where d(u)(+) and d(v)(-) are the out-degree and in-degree of the vertices u and v of D. When D 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 SO over the class D-n of digraphs with n non-isolated vertices, the classes C-n and S-n of connected and strongly connected digraphs on n vertices, respectively, the class of oriented trees OT (n) with n vertices, and the class O (n) of orientations of a fixed graph G.
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页数:5
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