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Query: "author" (Aleksander Kelenc) .

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1.
On metric dimensions of hypercubes
Aleksander Kelenc, Aoden Teo Masa Toshi, Riste Škrekovski, Ismael G. Yero, 2023, original scientific article

Abstract: In this note we show two unexpected results concerning the metric, the edge metric and the mixed metric dimensions of hypercube graphs. First, we show that the metric and the edge metric dimensions of $Q_d$ differ by at most one for every integer $d$. In particular, if $d$ is odd, then the metric and the edge metric dimensions of $Q_d$ are equal. Second, we prove that the metric and the mixed metric dimensions of the hypercube $Q_d$ are equal for every $d \ge 3$. We conclude the paper by conjecturing that all these three types of metric dimensions of $Q_d$ are equal when d is large enough.
Keywords: edge metric dimension, mixed metric dimension, metric dimension, hypercubes
Published in DiRROS: 19.03.2024; Views: 133; Downloads: 37
.pdf Full text (259,98 KB)

2.
Distance formula for direct-co-direct product in the case of disconnected factors
Aleksander Kelenc, Iztok Peterin, 2023, original scientific article

Abstract: Direct-co-direct product $G\circledast H$ of graphs $G$ and $H$ is a graph on the vertex set $V(G)\times V(H)$. Two vertices $(g,h)$ and $(g',h')$ are adjacent if $gg'\in E(G)$ and $hh'\in E(H)$ or $gg'\notin E(G)$ and $hh'\notin E(H)$. We show that if at most one factor of $G\circledast H$ is connected, then the distance between two vertices of $G\circledast H$ is bounded by three unless some small number of exceptions. All the exceptions are completely described which yields the distance formula.
Keywords: direct-co-direct product, distance, eccentricity, disconnected graphs
Published in DiRROS: 19.03.2024; Views: 94; Downloads: 54
.pdf Full text (450,88 KB)
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