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Try to find an axiomatization for each of the following classes of structures.If you can find one, write it down explicitly (you don’t need to prove that your axiomatization works). If you cannot find an axiomatization, just write that you don’t think it’s axiomatizable. (iii) Cycle graphs, i.e. undirected graphs that look like an undirected cycle of some length. (iv) Acyclic graphs, i.e. undirected graphs that do not contain any cycle. *A cycle graph is an undirected graph G := (V ,EG) such that V = {v0,v1,...vn} for some n, where v1,...,vn are pairwise distinct, v0 = vn, and EG = {(vi,vi+1),(vi+1,vi) : 0 ⩽ i < n}.

Try to find an axiomatization for each of the following classes of structures.If you can find one, write it down explicitly (you don’t need to prove that your axiomatization works). If you cannot find an axiomatization, just write that you don’t think it’s axiomatizable. (iii) Cycle graphs, i.e. undirected graphs that look like an undirected cycle of some length. (iv) Acyclic graphs, i.e. undirected graphs that do not contain any cycle. *A cycle graph is an undirected graph G := (V ,EG) such that V = {v0,v1,...vn} for some n, where v1,...,vn are pairwise distinct, v0 = vn, and EG = {(vi,vi+1),(vi+1,vi) : 0 ⩽ i < n}.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 48E
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Try to find an axiomatization for each of the following classes of structures.If you can find one, write it down explicitly (you don’t need to prove that your axiomatization works). If you cannot find an axiomatization, just write that you don’t think it’s axiomatizable.

(iii) Cycle graphs, i.e. undirected graphs that look like an undirected cycle of some length.

(iv) Acyclic graphs, i.e. undirected graphs that do not contain any cycle.

*A cycle graph is an undirected graph G := (V ,EG) such that V = {v0,v1,...vn} for some n, where v1,...,vn are pairwise distinct, v0 = vn, and EG = {(vi,vi+1),(vi+1,vi) : 0 ⩽ i < n}.

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