For a connected graph G on at least three vertices, the augmented Zagreb index (AZI) of G is defined as [Formula presented] being a topological index well-correlated with the formation heat of alkanes. A k-apex tree G is a connected graph admitting a k-subset X⊂V(G) such that G−X is a tree, while G−S is not a tree for any S⊂V(G) of cardinality less than k. By investigating some structural properties of k-apex trees, we identify the graphs minimizing the AZI among all k-apex trees on n vertices for k≥4 and n≥3(k+1). The latter solves an open problem posed in Cheng et al. (2021) [5].
The k-apex trees with minimum augmented Zagreb index / Liu, M.; Pang, S.; Belardo, F.; Ali, A.. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - 346:7(2023), pp. 1-20. [10.1016/j.disc.2023.113390]
The k-apex trees with minimum augmented Zagreb index
Belardo F.;
2023
Abstract
For a connected graph G on at least three vertices, the augmented Zagreb index (AZI) of G is defined as [Formula presented] being a topological index well-correlated with the formation heat of alkanes. A k-apex tree G is a connected graph admitting a k-subset X⊂V(G) such that G−X is a tree, while G−S is not a tree for any S⊂V(G) of cardinality less than k. By investigating some structural properties of k-apex trees, we identify the graphs minimizing the AZI among all k-apex trees on n vertices for k≥4 and n≥3(k+1). The latter solves an open problem posed in Cheng et al. (2021) [5].| File | Dimensione | Formato | |
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