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Further properties of trees with minimal atom-bond connectivity index. (English) Zbl 1474.05055

Summary: Let \(G = (V, E)\) be a graph the atom-bond connectivity (ABC) index is defined as the sum of weights \(((d_u + d_v - 2) / d_u d_v)^{1 / 2}\) over all edges \(u v\) of \(G\), where \(d_u\) denotes the degree of a vertex \(u\) of \(G\). In this paper, we determined a few structural features of the trees with minimal ABC index also we characterized the trees with \(\text{d} \text{i} \text{a} [T] = 2\) and minimal ABC index, where \([T]\) is induced by the vertices of degree greater than 2 in \(T\) and \(\text{d} \text{i} \text{a} [T]\) is the diameter of \([T]\).

MSC:

05C07 Vertex degrees
05C05 Trees
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
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