Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges

By Damir Vukicevic, Boris Furtula. 2009

797 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Organic Chemistry

View Paper: https://www.semanticscholar.org/paper/be4bebe5282233f1fa94a5d8a6fc6e452310a27b

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In Computational Theory and Mathematics

In Geometry and Topology

In Organic Chemistry

Citations in the corpus

Relation between second and third geometric–arithmetic indices of trees (2011, background): “The first geometric–arithmetic index (GA1) is defined as [9]:”
Three New/Old Vertex-Degree-Based Topological Indices (2014, background): “For a connected graph with m edges, GA(G) ≤ m, with equality if and only if G is regular [39].”
Survey on Geometric-Arithmetic Indices of Graphs (2011, methodology): “The first member [87] is the so-called geometric–arithmetic index GA1 , defined as GA1 = GA1(G) = ∑ uv∈E(G) √ du dv 1 2 (du + dv) (2)”
The fifth geometric-arithmetic index of bridge graph and carbon nanocones (2017, background): “By considering the degrees of vertices in G, Vukicevic and Furtula [18] developed the geometric-arithmetic index, shortly GA index, which is defined by GA(G) = ∑ uv∈E(G) 2 √ d(u)d(v) d(u) + d(v) , where d(u) and d(v) are the degrees of u and v, respectively.”
Vertex-Degree-Based Topological Indices Over Graphs (2014, background): “Many of the well-known topological indices are particular cases of this expression ([5],[6],[18],[19],[20]).”
On Vertex–Degree–Based Molecular Structure Descriptors (2011, background): “The geometric–arithmetic index GA is a recently invented structure descriptor [8] (see also [13,34–44]), defined as GA = GA(G) = ∑ uv∈E √ du dv (du + dv)/2 .”
Computing fifth geometric-arithmetic index for nanostar dendrimers (2011, background): “B. Zhou, I. Gutman, B. Furtula and Z. Du, On two types of geometric-arithmetic index, Chem.”
On geometric-arithmetic index (2010, methodology): “In [ 6 ], Vukiycevi´c and Furtula gave the lower and upper bounds for the GA index, identified the trees with the minimum and the maximum GA indices, which are the star and the path respectively, and then the path is the unique molecular tree (tree with maximum degree at most four used to model carb”