Graph Entropy for Adjacently and Non-Adjacently Configured Pentagonal Structure of Carbon Nanocones

Carbon nanocones possess exceptional properties compared to other nanomaterials, such as nanotubes, graphene etc. Hence they can be used as an alternative to other nanostructures. This work helps in determining various properties of the nanocone structure through topological descriptors. In this paper, various degree based topological descriptors along with its entropy measures are evaluated for adjacently and non-adjacently configured pentagonal structure of carbon nanocones. Carbon nanoparticles are gaining much importance in the contemporary world. Among which carbon nanocones have wide range of acceptance in the field of nanotechnology due to its effective properties and applications. Nanocones, also known as nanohorns are carbon networks which are planar in structure and has majority of hexagonal faces along with some nonhexagonal faces, which are most commonly pentagons. Nanocones which include pentagons in their structure can be referred to as adjacently or non- adjacently configured pentagonal structure of nanocones. Various topological descriptors for few nanocone classes were derived by researchers earlier, but not for the class of nanocones in this paper. Through this work, we try to vanish the research gap in this field. : The degree based descriptors and corresponding graph entropies for the adjacently and non-adjacently configured pentagonal structure of nanocones were determined, which further can be applied in quantitative structure – activity – property relationship studies. The concept of graph entropy is to assign a probability function to the edges in the chemical graph using the topological descriptor and it helps to characterise the complexity of graphs. We have employed the degree counting method and edge partition based on the vertices and edges of the adjacently and non-adjacently configured pentagonal nanocone structures to obtain the edge partitions and then using the corresponding mathematical expression, the degree based descriptors and its corresponding entropies were determined. Result: The analytically closed formulas to compute the degree based topological descriptors and graph entropies for any generation of the class of nanocone structures were obtained. In this work, the degree based descriptors and the corresponding graph entropies for the adjacently and non-adjacently configured pentagonal structure of carbon nanocones are determined applying the degree counting method and edge partition based on the vertices and edges. Also a graphical comparative study was also done with the help of obtained results. end.