Geodesic
A note on the distance-balanced property of generalized Petersen graphs
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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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, Klavžar, and Rall [Distance-balanced graphs, Ann. Comb. 12 (2008) 71–79] 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.
DOI : 10.37236/271
Classification : 05C12, 05C75
Mots-clés : generalized Petersen graph, distance-balanced graph 
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     author = {Rui Yang and Xinmin Hou and Ning Li and Wei Zhong},
     title = {A note on the distance-balanced property of generalized {Petersen} graphs},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/271},
     zbl = {1185.05055},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/271/}
}
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Rui Yang; Xinmin Hou; Ning Li; Wei Zhong. A note on the distance-balanced property of generalized Petersen graphs. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/271

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