On Isomorphisms of Tetravalent Cayley Digraphs over Dihedral Groups
Let $m$ be a positive integer. A group $G$ is said to be an $m$-DCI-group or an $m$-CI-group if $G$ has the $k$-DCI property or $k$-CI property for all positive integers $k$ at most $m$, respectively. Let $G$ be a dihedral group of order $2n$ with $n\geq 3$. Qu and Yu proved that $G$ is an $m$-DCI-g...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
17.07.2024
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Subjects | |
Online Access | Get full text |
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Summary: | Let $m$ be a positive integer. A group $G$ is said to be an $m$-DCI-group or
an $m$-CI-group if $G$ has the $k$-DCI property or $k$-CI property for all
positive integers $k$ at most $m$, respectively. Let $G$ be a dihedral group of
order $2n$ with $n\geq 3$. Qu and Yu proved that $G$ is an $m$-DCI-group or
$m$-CI-group, for every $m\in \{1,2,3\}$, if and only if $n$ is odd. In this
paper, it is shown that $G$ is a $4$-DCI-group if and only if $n$ is odd and
not divisible by $9$, and $G$ is a $4$-CI-group if and only if $n$ is odd. |
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DOI: | 10.48550/arxiv.2407.12457 |