The first geometric-arithmetic index of graph operations

Abstract

The first geometric-arithmetic (G-A) index of a graph G is defined as GA(1)(G) = Sigma u(,v is an element of E(G))2 root d(G)(u)d(G)(v)/d(G)(u)+d(G)(v), where d(G)(u) uGd is the degree of the vertex u. Expressions for the first AG. index are obtained for semitotal-line graph (middle graph), semitotal-point graph, total graph as well as eight kinds of total transformation graphs G(xyz).