The Minimal-ABC Trees With 1 -Branches II

The atom-bond connectivity (ABC) index is one of the most investigated degree-based molecular structure descriptors with a variety of chemical applications. For a given graph G=(V,E) , the ABC index is defined as ABC(G)=\sum _{uv\in E} {(d_{u}+d_{v}-2)/(d_{u}d_{v})}^{1/2} , where d_{u} denotes t...

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Bibliographic Details
Published in:IEEE access 2018, Vol.6, p.66350-66366
Main Authors: Du, Zhibin, Dimitrov, Darko
Format: Article
Language:English
Subjects:
Atom-bond connectivity index
Chemicals
Compounds
Context modeling
extremal graphs
greedy trees
Indexes
Mathematics
minimal-ABC trees
Organic chemicals
Thermodynamics
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Summary:The atom-bond connectivity (ABC) index is one of the most investigated degree-based molecular structure descriptors with a variety of chemical applications. For a given graph G=(V,E) , the ABC index is defined as ABC(G)=\sum _{uv\in E} {(d_{u}+d_{v}-2)/(d_{u}d_{v})}^{1/2} , where d_{u} denotes the degree of the vertex u , and uv is the edge incident to the vertices u and v . It is known that a minimal-ABC tree (a tree with the minimal value of the ABC index) cannot contain more than four so-called B_{1} -branches (the figuration for B_{1} -branch see Fig. 1 ). Recently, it was shown that a minimal-ABC tree of order larger than 19 contains neither three nor four B_{1} -branches. Here, we further improve those results by showing that a minimal-ABC tree of order larger than 122 cannot contain also one B_{1} -branch. Moreover, we have proven that a minimal-ABC tree of order larger than 122 can contain only two B_{1} -branches and that only in a combination with one B_{2} -branch (the figuration can also see B_{3}^{**} -branch in Fig. 1 ).
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2018.2879121