Lights Out on Petersen Graphs
نویسندگان
چکیده
We establish some preliminary results for Sutner’s σ game, i.e. “Lights Out,” played on the generalized Petersen graph P (n, k). While all regular Petersen graphs admit game configurations that are not solvable, we prove that every game on the P (2n, n) graph has a unique solution. Moreover, we introduce an exceedingly simple strategy for finding the solution to any game on these graphs. Surprisingly, this same strategy is shown to work on a few other Petersen graphs, and on some other related graphs.
منابع مشابه
Graceful labelings of the generalized Petersen graphs
A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...
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