Bounds of Rede ned Zagreb indices for F-Sum of Graphs, F = Q or T

Abstract

Rede ned Zagreb indices are new graph invariants, which is the degree based topological index ReZG1(G) = Σ uv2E(G) du+dv dudv , ReZG2(G) = Σ uv2E(G) dudv du+dv and ReZG3(G) = Σ uv2E(G)(dudv) (du + dv). Eliasi and Taeri introduced four new operations based on graphs S(G), R(G), Q(G) and T(G), which are also known as F- sum of graphs, where F= S, Q, R and T. In this paper, we establish bounds of the rede ned Zagreb indices for for F-Sum of Graphs, where F = Q or T.