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|Title:||The ABC index conundrum|
Salehi Nowbandegani P.
|Abstract:||The atom-bond connectivity (ABC) index of a graph G is defined as the sum over all pairs of adjacent vertices u; ν, of the terms √[d(u) + d(ν) - 2]=[d(u) d(ν)], where d(ν) denotes the degree of the vertex ν of the graph G. Whereas the finding of the graphs with the greatest ABC-value is an easy task, the characterization of the graphs with smallest ABC-value, in spite of numerous attempts, is still an open problem. What only is known is that the connected graph with minimal ABC index must be a tree, and some structural features of such trees have been determined. Several conjectures on the structure of the minimal-ABC trees, were disproved by counterexamples. In this review we present the state of art of the search for minimal-ABC trees, and provide a complete bibliography on ABC index.|
|Appears in Collections:||Faculty of Science, Kragujevac|
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