• MULTIPLICATIVE HYPER-ZAGREB INDICES AND COINDICES OF GRAPHS: COMPUTING THESE INDICES OF SOME NANOSTRUCTURES

Abstract

In this paper, we introduce the first and second multiplicative hyper-Zagreb indices of a graph. The first multiplicative hyper-Zagreb index is defined as the product of squares of the sum of the degrees of pairs of adjacent vertices. The second multiplicative hyper- Zagreb index is defined as the product of squares of the product of the degrees of pairs of adjacent vertices. Also we introduce the first and second multiplicative hyper-Zagreb coindices of a graph. In this paper, the first and second multiplicative hyper-Zagreb indices of cycles, complete graphs, complete bipartite graphs and r-regular graphs are determined. Also we compute exact formulas of the multiplicative hyper-Zagreb indices for    G = TUSC₄C₈(S) nanotubes, G₁ = VPHX [m, n] nanotues and G₂ = VPHY [m, n] nanotorus.