{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T06:54:50Z","timestamp":1769928890929,"version":"3.49.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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 $G\\wr H$ 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 $S_n\\wr H$ 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 $S_n\\wr S_m$ in terms of tail conditional expectations of an associated binomial distribution.<\/jats:p>","DOI":"10.37236\/8071","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T02:15:46Z","timestamp":1578622546000},"source":"Crossref","is-referenced-by-count":9,"title":["Total Distance, Wiener Index and Opportunity Index in Wreath Products of Star Graphs"],"prefix":"10.37236","volume":"26","author":[{"given":"Matteo","family":"Cavaleri","sequence":"first","affiliation":[]},{"given":"Alfredo","family":"Donno","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3038-3957","authenticated-orcid":false,"given":"Andrea","family":"Scozzari","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,2,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p21\/7780","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p21\/7780","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:18:20Z","timestamp":1579216700000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i1p21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,8]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/8071","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,8]]},"article-number":"P1.21"}}