Some Problems On Zagreb Eccentricity Indices Of Graphs

For an undirected connected graph G,let V(G)and E(G)denote its vertex set and edge set,respectively.The first Zagreb eccentricity index is defined as ?1(G)=?u?V(G)eG2(u),the second Zagreb eccentricity index is defined as ?2(G)=?uv?E(G)eG(u)eG(v),where eG(u)denotes the eccentricity of u in G,which is equal to the largest distance from u to other vertices.The first and second eccentricity indices play an important role in mathematical chemistry.Let C(n,k)be the class of all cacti of order n with k cycles.Let A(n,m,d)be the class of bipartite of order n,edge m with diameter d.In this paper,we establish sharp lower bounds on Zagreb eccentricity indices of graph in C(n,k)and determine the corresponding extremal graphs.What's more,we characterize the graphs in C(n,k)with maximal Zagreb eccentricity indices,where 0?k?[N-1/2].At last,we establish lower bounds on the second Zagreb eccentricity index of graph in A(n,m,d)and determine the corresponding extremal graphs.