The Second Reformulated Zagreb Index And The Connective Eccentricity Index Of Some Graphs

Zagreb indices and connective eccentricity index as classical topological indices,they are attractive distance-based topological indices,and they can reflect the extent of branch-ing of a molecular structure.In 2004,the authors Milicevic et al.introduced the reformu-lated Zagreb indices.In 2012,Zhou et al.characterized the extremal graph of unicyclic graphs with the first reformulated Zagreb indices.Recently,Ji et al.first introduced some graph operations which increase or decrease this index and determined the extremal trees,unicyclic and bicyclic graphs with minimum and maximum of the first reformulated Zagreb index,respectively.In 2000,the authors Gupta et al.introduced the connective eccentricity index of a graph G.In this paper,first we will use the similar way and the least graph operation to determine the maximum and minimum indices for the second reformulated Zagreb indices of trees,unicyclic and bicyclic graphs,respectively.Then we determine the maximal graphs from bicyclic graph with given matching number with respect to connective eccentricity index.In this paper,The specific structure is arranged as follows:In the first chapter,we introduce the definition and the background of the second reformulated Zagreb index and the connective eccentricity index,and give the basic no-tations which will be related to this paper.In the second chapter,we use the graph operation to determine the maximum and minimum indices for the second reformulated Zagreb indices of trees,unicyclic and bicyclic graphs,respectively.In the three chapter,we determine the maximal graphs from bicyclic graph with given matching number with respect to connective eccentricity index.