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Undirected edge geography games on stacked prism graphs
Abstract
The undirected edge geography is a two-player combinatorial game on an undirected graph. The players start at the root vertex and alternately move the root along an incident edge to its other endpoint and then delete that edge. The first player who has no remaining move is the loser. For positive integers m and n where m≥ 3, the stacked prism graph is SP(m,n)=Cm□ Pn. In this paper, we completely determine the winner of the game on SP(2m,n) for m≥ 2 and SP(m,2) for m≥ 3, and provide a winning strategy for the winner.
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BibTeX
@misc{sereekiatdilok2026undirected,
title = {{Undirected edge geography games on stacked prism graphs}},
author = {Tharit Sereekiatdilok and Panupong Vichitkunakorn},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11409},
eprint = {2609.11409},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11409},
}
RIS
TY - UNPB
TI - Undirected edge geography games on stacked prism graphs
AU - Tharit Sereekiatdilok
AU - Panupong Vichitkunakorn
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11409
UR - https://arxiv.org/abs/2609.11409
AB - The undirected edge geography is a two-player combinatorial game on an undirected graph. The players start at the root vertex and alternately move the root along an incident edge to its other endpoint and then delete that edge. The first player who has no remaining move is the loser. For positive integers m and n where m≥ 3, the stacked prism graph is SP(m,n)=C_m□ P_n. In this paper, we completely determine the winner of the game on SP(2m,n) for m≥ 2 and SP(m,2) for m≥ 3, and provide a winning strategy for the winner.
ER -