Cacti With Wiener Index And Hyper-Wiener Index

Topological index has always been an important research topic in chemical graph theory,which has always been a hot issue for scholars to study.Its research and development prospects are very broad,and its main results can be used to study the properties of molecular structures in chemistry.In this paper,we study two kinds of topological index hyper-Wiener index and Wiener index in cactus graph.The first chapter introduces the research background,basic knowledge and research status at home and abroad,and the main conclusions of this paper are briefly described.The second chapter introduces two graph transformation operations and the corresponding four lemmas.By comparison,we gave the second-minimum and third-minimum Wiener indices among cactus,and characterize the corresponding extremal graphs as well.In Chapter 3,we studied the hyper-Wiener index of the cactus using the transformation operations defined in the previous chapter.By comparison,the hyper-Wiener index of cactus was studied,and we gave the second-minimum and third-minimum hyper-Wiener indices among cactus,and characterize the corresponding extremal graphs as well.