On Sombor Index

Abstract

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.

On Sombor energy of graphs

“…Recently, Gutman et al [15] defined new degree-based indices, called the Sombor index, which is one of the trending areas in the present graphtheoretical research. The details of this new index we refer to [16][17][18][19][20][21][22][23][24][25]. In [26], the chemical applicability of Sombor indices had been studied.…”

More on Sombor indices of chemical graphs and their applications to the boiling point of benzenoid hydrocarbons

“…The Sombor index of G is defined as [2] whereas the reduced Sombor index is [2] Recent results of Sombor index can be found in References [2–19].…”

The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs

“…Das, Cevik, Cangul and Shang presented lower and upper bounds on the Sombor index of graphs by using some graph parameters and obtain several relations on Sombor index with the first and second Zagreb indices of graphs [7]. More results of Sombor indices can be found in [2,3,[8][9][10][11][12][13][14][15][16][17]37]. In Section 2, we study the expected values of the Sombor indices in the random hexagonal chains and random phenylene chains, and make a comparison between the expected values.…”

“…[6], the extremal values of the Sombor index in unicyclic and bicyclic graphs were studied. Das, Cevik, Cangul and Shang presented lower and upper bounds on the Sombor index of graphs by using some graph parameters and obtain several relations on Sombor index with the first and second Zagreb indices of graphs [7]. More results of Sombor indices can be found in [2, 3, 8–17, 37].…”