On the Maximum ABC Index of Graphs With Prescribed Size and Without Pendent Vertices

The atom-bond connectivity (ABC) index is one of the most actively studied degree-based graph invariants, which are found in a vast variety of chemical applications. For a simple graph G, it is defined as ABC(G) = Σ uv∈E(G) ((d(u) + d(v) - 2)/(d(u)d(v))) 1/2 , where d(v) denotes the degree ofa verte...

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Bibliographic Details
Published in:IEEE access 2018-01, Vol.6, p.27604-27616
Main Authors: Zehui Shao, Pu Wu, Xiujun Zhang, Dimitrov, Darko, Jia-Bao Liu
Format: Article
Language:English
Subjects:
3G mobile communication
ABC index
Apexes
Atom–bond connectivity index
Chemicals
extremal graph
Graph theory
Graphs
Indexes
Information science
Mathematics
Physics
STEM
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Summary:The atom-bond connectivity (ABC) index is one of the most actively studied degree-based graph invariants, which are found in a vast variety of chemical applications. For a simple graph G, it is defined as ABC(G) = Σ uv∈E(G) ((d(u) + d(v) - 2)/(d(u)d(v))) 1/2 , where d(v) denotes the degree ofa vertex v of G. Recently in [17] graphs with n vertices, 2n - 4 and 2n - 3 edges, and maximum ABC index were characterized. Here, we consider the next, more complex case, and characterize the graphs with n vertices, 2n - 2 edges, and maximum ABC index.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2018.2831910