On the second Zagreb eccentricity indices of graphs

摘要

For a connected graph G, the second Zagreb eccentricity index of G is defined as ξ2(G)=∑uv∈E(G)eG(u)eG(v), where eG(u) denotes the eccentricity of u in G. In this paper, we give a graft transformation to increase the second Zagreb eccentricity indices of graphs, and as applications, we determine n-vertex bicyclic graphs with maximum and second maximum second Zagreb eccentricity indices, respectively.