Non-$\ell$-distance-balanced generalized Petersen graphs $GP(n,3)$ and $GP(n,4)$

Gang Ma, Jianfeng Wang, Sandi Klavžar

A connected graph $G$ of diameter $\mathrm{diam}(G)\ge \ell$ 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…