Expected values of Sombor indices and their entropy measures for graphene

Graph theory plays a crucial role in various applications of mathematics and applied sciences. One specialised branch of graph theory is mathematical chemistry, which focuses on mathematical modelling and analysing chemical compounds and their properties. In this context, graphs are used to represent the structural and topological features of molecules, enabling chemists to gain insights into chemical reactions and make predictions about molecular properties. Recently, new versions of Sombor indices have been introduced using a geometric approach. This article specifically focuses on entropy-based variations of these Sombor indices, which includes SO, SOred, SOavg, (SO)-S-m, SO3 and SO4, in the context of graphene sheet. Graphene has gained significant attention in the scientific and technological communities due to its exceptional properties. It finds widespread applications in diverse fields such as nanotechnology, electronics, energy storage, sensors, materials science and optoelectronics. Given the promising applications of graphene, it becomes essential to theoretically analyse its structure. Molecular descriptors play a crucial role, as they are strongly linked to various characteristics of chemical compounds. To better understand the Sombor indices, this article graphically represents their entropy measures.{GRAPHICAL ABSTRACT}