The undirected power graph \$\$\textbackslashmathscr \G\(S)\$\$of a semigroup S is an undirected graph with vertex set S where two vertices \$\$u,v\textbackslashin S\$\$are adjacent if and only if there is a positive integer m such that \$\$uˆ\m\=v\$\$or \$\$vˆ\m\=u\$\$. Here, we investigate the power graphs of a class of abelian groups and answer, in this case, the question whether or not the power graph is Hamiltonian.
%0 Journal Article
%1 santiagoarguello2023hamiltonicity
%A Santiago Arguello, Anahy
%A Montellano-Ballesteros, Juan José
%A Stadler, Peter F.
%D 2023
%J Journal of Algebraic Combinatorics
%K imported
%N 1
%P 313--328
%R 10.1007/s10801-022-01172-9
%T Hamiltonicity in power graphs of a class of abelian groups
%U https://doi.org/10.1007/s10801-022-01172-9
%V 57
%X The undirected power graph \$\$\textbackslashmathscr \G\(S)\$\$of a semigroup S is an undirected graph with vertex set S where two vertices \$\$u,v\textbackslashin S\$\$are adjacent if and only if there is a positive integer m such that \$\$uˆ\m\=v\$\$or \$\$vˆ\m\=u\$\$. Here, we investigate the power graphs of a class of abelian groups and answer, in this case, the question whether or not the power graph is Hamiltonian.
@article{santiagoarguello2023hamiltonicity,
abstract = {The undirected power graph \$\${\textbackslash}mathscr \{G\}(S)\$\$of a semigroup S is an undirected graph with vertex set S where two vertices \$\$u,v{\textbackslash}in S\$\$are adjacent if and only if there is a positive integer m such that \$\$u{\textasciicircum}\{m\}=v\$\$or \$\$v{\textasciicircum}\{m\}=u\$\$. Here, we investigate the power graphs of a class of abelian groups and answer, in this case, the question whether or not the power graph is Hamiltonian.},
added-at = {2024-10-02T13:52:45.000+0200},
author = {Santiago Arguello, Anahy and Montellano-Ballesteros, Juan José and Stadler, Peter F.},
biburl = {https://puma.scadsai.uni-leipzig.de/bibtex/2cc3ba8bb86047baf58756b60809d755a/scadsfct},
doi = {10.1007/s10801-022-01172-9},
interhash = {9f70e109d5343d7a1b7ad0686d3ab6b9},
intrahash = {cc3ba8bb86047baf58756b60809d755a},
issn = {1572-9192},
journal = {Journal of Algebraic Combinatorics},
keywords = {imported},
month = feb,
number = 1,
pages = {313--328},
timestamp = {2024-10-02T13:52:45.000+0200},
title = {Hamiltonicity in power graphs of a class of abelian groups},
url = {https://doi.org/10.1007/s10801-022-01172-9},
volume = 57,
year = 2023
}