Research On The Unicyclic Chart Of The Minimal ABC Index

Topological index is a very important research topic in chemical graph theory.Its research and development prospect is very extensive.It has important applications in chemical molecular structure.The topological index is the mathematical descriptor of the chemical molecular structure,and the topological index of a molecular graph realizes the numerical value of the molecular structure information.The atomic connectivity index(ABC index)of a graph is a topological index based on the degrees of the vertices.It is applied to chemistry.In this paper,the minimal ABC index of the unicycle graph is studied.The main results are as follows:In the first chapter,introduces the historical background and significance of the ABC index,and gives some basic concepts,some related conclusions and the main conclusions of this paper.In the second chapter,we give the structural properties of the unicycle graph with minimal ABC index,and prove the relation between the ABC index of unicycle graph and the tricyclic graph through graph transformation and fraction comparison.In the third chapter,by searching for the corresponding pivot column of the unicycle graph,and the minimal ABC index of the unicycle graph in the tricyclic graph is depicted.