Abstract
Let G be a connected graph with edge set $E (G)$ . The atom-bond connectivity index (ABC index for short) is defined as $ABC (G) = \sum_{uv \in E (G)} \sqrt{ \frac{d_{G} (u)+d_{G} (v)-2}{d_{G} (u) d_{G} (v)} }$ , where $d_{G} (u)$ denotes the degree of vertex u in G. The research of ABC index of graphs is active these years, and it has found a lot of applications in a variety of fields. In this paper, we will focus on the relationship between ABC index and radius of connected graphs. In particular, we determine the upper and lower bounds of the difference between ABC index and radius of connected graphs.
Highlights
1 Introduction Let G be a connected graph with vertex set V (G) and edge set E(G)
In, Estrada et al [ ] proposed a topological index based on the degrees of vertices of graphs, which is called the atom-bond connectivity index (ABC index for short)
Xing et al [ ] presented an upper bound for the ABC index of connected graphs with fixed number of
Summary
Let G be a connected graph with vertex set V (G) and edge set E(G). For v ∈ V (G), let dG(v) denote the degree of vertex v in G.In chemical graph theory, we usually use a graph to represent a molecule graph. 1 Introduction Let G be a connected graph with vertex set V (G) and edge set E(G). Xing et al [ ] presented an upper bound for the ABC index of connected graphs with fixed number of More results on ABC index of graphs can be found in [ – ], especially for trees [ – ].
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