First and Second Zagreb Eccentricity Indices of Thorny Graphs

The Zagreb eccentricity indices are the eccentricity reformulation of the Zagreb indices. Let H be a simple graph. The first Zagreb eccentricity index (E-1(H)) is defined to be the summation of squares of the eccentricity of vertices, i.e., E-1(H) = Sigma(u epsilon v(H)) epsilon H-2(u).The second Zagreb eccentricity index (E2(H)) is the summation of product of the eccentricities of the adjacent vertices, i.e.,(E-2(H) = Sigma(uv epsilon E)(H)epsilon(H)(u)epsilon(H()v).We obtain the thorny graph H by attaching thorns i.e.,vertices of degree one to every vertex of H. In this paper,we will find closed formulation for the first Zagreb eccentricity index and second Zagreb eccentricity index of different well known classes of thorny graphs.