A group splits over a subgroup if is either a free product with amalgamation or an HNN-extension . We invoke Bass–Serre theory to classify all infinite groups which admit cubic Cayley graphs of connectivity two in terms of splittings over a subgroup.
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Keywords: Free product with amalgamation, HNN-extension, Bass–Serre theory, planar graphs.
@article{ALCO_2021__4_6_971_0, author = {Miraftab, Babak and Stavropoulos, Konstantinos}, title = {Splitting groups with cubic {Cayley} graphs of connectivity two}, journal = {Algebraic Combinatorics}, pages = {971--987}, publisher = {MathOA foundation}, volume = {4}, number = {6}, year = {2021}, doi = {10.5802/alco.188}, language = {en}, url = {http://www.numdam.org/articles/10.5802/alco.188/} }
TY - JOUR AU - Miraftab, Babak AU - Stavropoulos, Konstantinos TI - Splitting groups with cubic Cayley graphs of connectivity two JO - Algebraic Combinatorics PY - 2021 SP - 971 EP - 987 VL - 4 IS - 6 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.188/ DO - 10.5802/alco.188 LA - en ID - ALCO_2021__4_6_971_0 ER -
%0 Journal Article %A Miraftab, Babak %A Stavropoulos, Konstantinos %T Splitting groups with cubic Cayley graphs of connectivity two %J Algebraic Combinatorics %D 2021 %P 971-987 %V 4 %N 6 %I MathOA foundation %U http://www.numdam.org/articles/10.5802/alco.188/ %R 10.5802/alco.188 %G en %F ALCO_2021__4_6_971_0
Miraftab, Babak; Stavropoulos, Konstantinos. Splitting groups with cubic Cayley graphs of connectivity two. Algebraic Combinatorics, Volume 4 (2021) no. 6, pp. 971-987. doi : 10.5802/alco.188. http://www.numdam.org/articles/10.5802/alco.188/
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