# On $\ell$-distance balanced product graphs

10 Jun 2020 Jerebic Janja Klavžar Sandi Rus Gregor

A graph $G$ is $\ell$-distance-balanced if for each pair of vertices $x$ and $y$ at distance $\ell$ in $G$, the number of vertices closer to $x$ than to $y$ is equal to the number of vertices closer to $y$ than to $x$. A complete characterization of $\ell$-distance-balanced corona products is given and a characterization of lexicographic products for $\ell \ge 3$, thus complementing known results for $\ell\in \{1,2\}$ and correcting an earlier related assertion... (read more)

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