On metric dimension of edge comb product of vertex-transitive graphs

Maryati, Tita Khalis; Sobiruddin, Dindin; Fatra, Maifalinda; Hadiputra, Fawwaz Fakhrurrozi

doi:10.22108/toc.2024.133850.1991

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	On metric dimension of edge comb product of vertex-transitive graphs
Transactions on Combinatorics
مقاله 6، دوره 14، شماره 1، خرداد 2025، صفحه 45-64 اصل مقاله (629.31 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2024.133850.1991
نویسندگان
Tita Khalis Maryati¹؛ Dindin Sobiruddin¹؛ Maifalinda Fatra¹؛ Fawwaz Fakhrurrozi Hadiputra^* ²
¹Department of Mathematics Education, Syarif Hidayatullah State Islamic University Jakarta, Indonesia
²Department of Mathematics, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Indonesia
چکیده
Suppose finite graph $G$ is simple, undirected and connected. If $W$ is an ordered set of the vertices such that $\|W\| = k$, the representation of a vertex $v$ is an ordered $k$-tuple consisting distances of vertex $v$ with every vertices in $W$. The set $W$ is defined as resolving vertex of $G$ if the $k$-tuples of every two vertices are distinct. Metric dimension of $G$, which is denoted by $dim(G)$, is the lowest size of $W$. In this paper, we provide a sharp lower bound of metric dimension for edge comb product graphs $G \cong T$ ▷_e $H$ where $T$ is a tree graph and $H$ is a vertex-transitive graph. Moreover, we determine the exact value of metric dimension for edge comb product graphs $G \cong T$ ▷_e $Ci_n(1,2)$ where $Ci_n(1,2)$ is a circulant graph.
کلیدواژه‌ها
Metric Dimension؛ Edge Comb Product؛ Trees؛ Vertex-Transitive

مراجع
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On metric dimension of edge comb product of vertex-transitive graphs