Name
Abstract | ||
|---|---|---|
In the last decades much attention has turned towards centrality measures on graphs. The Wiener index and the total distance are key tools to investigate the median vertices, the distance-balanced property and the opportunity index of a graph. This interest has recently been addressed to graphs obtained via classical graph products like the Cartesian, the direct, the strong and the lexicographic product. We extend this study to a relatively new graph product, that is, the wreath product. In this paper, we compute the total distance for the vertices of an arbitrary wreath product graph G (sic) H in terms of the total distances in H and of some distance-based indices of G. We explicitly compute these indices for the star graph S-n, providing a closed formula for the total distances in S-n (sic) H when H is complete or a star. As a consequence, we obtain the Wiener index of these graphs, we characterize the median and the central vertices, and finally we give an upper and a lower bound for the opportunity index of S-n (sic) S-m, in terms of tail conditional expectations of an associated binomial distribution. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.37236/8071 | ELECTRONIC JOURNAL OF COMBINATORICS |
Field | DocType | Volume |
Discrete mathematics,Graph,Combinatorics,Wiener index,Mathematics | Journal | 26 |
Issue | ISSN | Citations |
1 | 1077-8926 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Matteo Cavaleri | 1 | 0 | 2.03 |
| Alfredo Donno | 2 | 27 | 8.03 |
| Andrea Scozzari | 3 | 0 | 0.34 |