The First General Zagreb Index Of Unicyclic Graph With Given Girth

Zagreb indices are classical topological indices,including the first Zagreb index and the second Zagreb index,and they can reflect the extent of branching of a molecular structure.Since the concept of the two indices was proposed,they attracted many people to study extensively,and lots of properties were gradually discovered.Later,Li and Zheng proposed the concept of the first general Zagreb index,and some properties of special graphs were discussed.In this paper,we study the extreme value of the first general Zagreb index for unicyclic graph with given girth.The paper contains the following three sections:In the first chapter,we introduce the definition and the background of the first general Zagreb index,and give the basic notations which will be related to this paper.In the second chapter,we study the first general Zagreb index in the unicyclic graph with given girth,and have achieved the unicyclic graph with given girth g which have the largest and the smallest values of the index.In the three chapter,we investigate the first general Zagreb index in the unicyclic graph with given girth,and have obtained the unicyclic graph with given girth g which have the second largest and smallest values of the index.