The conjecture on distance-balancedness of generalized Petersen graphs holds when internal edges have jumps $3$ or $4$Ma, Gang (Avtor) Wang, JianFeng (Avtor) Klavžar, Sandi (Avtor) distance-balanced graph$\ell$-distance-balanced graphgeneralized Petersen graphdiameterA connected graph $G$ with ${\rm diam}(G) \ge \ell$ is $\ell$-distance-balanced if $|W_{xy}|=|W_{yx}|$ for every $x,y\in V(G)$ with $d_{G}(x,y)=\ell$, where $W_{xy}$ is the set of vertices of $G$ that are closer to $x$ than to $y$. Miklavič and Šparl [Discrete Appl. Math. 244 (2018), 143--154] conjectured that if $n > n_k$ where where $n_k = 11$ if $k = 2$, $n_k = (k+1)^2$ if $k$ is odd, and $n_k = k(k +2)$ if $k \ge 4$ is even, then the generalized Petersen graph $GP(n,k)$ is not $\ell$-distance-balanced for any $1\le \ell<{\rm diam}(GP(n,k))$. In the seminal paper, the conjecture was verified for $k=2$. In this paper we prove that the conjecture holds for $k=3$ and for $k=4$.20252025-11-07 09:01:14Članek v reviji175773UDK: 519.17ISSN pri članku: 1669-9637DOI: 10.33044/revuma.4824COBISS_ID: 256284675sl