Name
Abstract | ||
|---|---|---|
The Augmented Zagreb index of a graph G is defined to be AZI (G) = sigma(uv epsilon E(G)) (d(u)d(v)/d(u)+d(v)-2)(3), where E (G) is the edge set of G, d (u) and d (v) are the degrees of the vertices u and v of edge uv. It is one of the most valuable topological indices used to predict the structure-property correlations of organic compounds. It is well known that the star is the unique tree having minimal AZI among trees. However, the problem of finding the tree with maximal AZI is still open and seems to be a very difficult problem. A recent conjecture, posed in the recent paper [IEEE Access, vol. 6, pp. 69335-69341, 2018], states that the balanced double star is the tree with maximal AZI among all trees with n vertices, for all n >= 19. Let omega (n, p) be the set of trees with n vertices and p branching vertices. In this paper we consider the maximal value problem of AZI over omega (n, p). We first show that under a certain condition, the problem reduces to finding the maximal value of AZI over omega(1) (n, p), the set of trees in omega (n, p) with no vertices of degree 2. Then we rely on this result to find the trees with maximal value of AZI over omega (n, p), when p = 2 and 3. In particular, we deduce that the conjecture holds for all trees with at most 3 branching vertices. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1109/ACCESS.2019.2946131 | IEEE ACCESS |
Keywords | DocType | Volume |
Indexes, Licenses, Correlation, Organic compounds, Numerical models, Chemical compounds, Augmented Zagreb index, extremal trees | Journal | 7 |
ISSN | Citations | PageRank |
2169-3536 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Roberto Cruz | 1 | 0 | 0.34 |
| Juan Daniel Monsalve | 2 | 0 | 0.34 |
| Juan Rada | 3 | 36 | 10.02 |