On the geometric-arithmetic index by decompositions-CMMSE Articles uri icon

publication date

  • September 2016

start page

  • 1

end page

  • 16

international standard serial number (ISSN)

  • 0259-9791

electronic international standard serial number (EISSN)

  • 1572-8897

abstract

  • The concept of geometric&-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. There are many papers studying different kinds of indices (as Wiener, hyper&-Wiener, detour, hyper&-detour, Szeged, edge&-Szeged, PI, vertex&-PI and eccentric connectivity indices) under particular cases of decompositions. The main aim of this paper is to show that the computation of the geometric-arithmetic index of a graph G is essentially reduced to the computation of the geometric-arithmetic indices of the so-called primary subgraphs obtained by a general decomposition of G. Furthermore, using these results, we obtain formulasfor the geometric-arithmetic indices of bridge graphs and other classes of graphs, likebouquet of graphs and circle graphs. These results are applied to the computation