Open AccessSome mathematical properties of the geometric-arithmetic index/coindex of graphs
Author(s) -
Stanko Stankov,
Marjan Matejić,
Igor Ž. Milovanović,
Emina I. Milovanović
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2115045s
Subject(s) - mathematics , combinatorics , vertex (graph theory) , graph , simple graph , discrete mathematics , topological index , degree (music) , arithmetic , physics , acoustics
Let G = (V,E), V = {1,2,...,n}, be a simple connected graph of order n, size m with vertex degree sequence d1 ? d2 ? ... ? dn > 0, di = d(vi). The geometric-arithmetic topological index of G is defined as GA(G) = ? i~j 2? didj/di+dj, whereas the geometric-arithmetic coindex as GA?(G) = ? i~/j 2 ? didj/di+dj . New lower bounds for GA(G) and GA(G) in terms of some graph parameters and other invariants are obtained.