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- W2978756041 abstract "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 $ellin {1,2}$ and correcting an earlier related assertion. A sufficient condition on $H$ which guarantees that $K_n ,square, H$ is $ell$-distance-balanced is given and it is proved that if $K_n ,square, H$ is $ell$-distance-balanced, then $H$ is an $ell$-distance-balanced graph. A known characterization of $1$-distance-balanced graphs is extended to $ell$-distance-balanced graphs, again correcting an earlier claimed assertion." @default.
- W2978756041 created "2019-10-10" @default.
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- W2978756041 date "2019-10-04" @default.
- W2978756041 modified "2023-09-27" @default.
- W2978756041 title "On $ell$-distance balanced product graphs" @default.
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