{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:23:38Z","timestamp":1759335818978,"version":"3.41.2"},"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>A graph $G$ is said to be distance-balanced if for any edge $uv$ of $G$, the number of vertices closer to $u$ than to $v$ is equal to the number of vertices closer to $v$ than to $u$. Let $GP(n,k)$ be a generalized Petersen graph. Jerebic, Klav\u017ear, and Rall [Distance-balanced graphs, Ann. Comb. 12 (2008) 71\u201379] conjectured that: For any integer $k\\geq 2$, there exists a positive integer $n_0$ such that the  $GP(n,k)$ is not distance-balanced for every integer $n\\geq n_0$. In this note, we give a proof of this conjecture.<\/jats:p>","DOI":"10.37236\/271","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:23:43Z","timestamp":1578716623000},"source":"Crossref","is-referenced-by-count":12,"title":["A Note on the Distance-Balanced Property of Generalized Petersen Graphs"],"prefix":"10.37236","volume":"16","author":[{"given":"Rui","family":"Yang","sequence":"first","affiliation":[]},{"given":"Xinmin","family":"Hou","sequence":"additional","affiliation":[]},{"given":"Ning","family":"Li","sequence":"additional","affiliation":[]},{"given":"Wei","family":"Zhong","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,11,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n33\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:03:54Z","timestamp":1579305834000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1n33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11,24]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/271","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,11,24]]},"article-number":"N33"}}