MHB Fleury's Algorithm: Finding Next Edge

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Fleury's Algorithm is applied to determine the next edge to travel from a specific vertex in a graph after three edges have been deleted. The discussion emphasizes the importance of identifying all possible edges that can be traversed next from the starred vertex. Participants highlight the need for clarity in graph representation, as the absence of visual aids and context for the vertex labels can lead to confusion. The focus remains on ensuring that the algorithm is correctly implemented to find valid paths. Overall, understanding the graph's structure is crucial for effectively using Fleury's Algorithm.
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Using Fleury’s Algorithm in the graph to the bottom left, I deleted three edges and I got the graph to the bottom right. If I am currently at the starred vertex, list all possibilities for the edge I should travel next.

A B Left graph
3

2
C D
1E F

A
B

Right graph

C D

E F
 
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You did not include pictures of the graph. Also, the letters (A, B, E, F, etc.) that follow the first paragraph don't make sense without a context.
 
I'm taking a look at intuitionistic propositional logic (IPL). Basically it exclude Double Negation Elimination (DNE) from the set of axiom schemas replacing it with Ex falso quodlibet: ⊥ → p for any proposition p (including both atomic and composite propositions). In IPL, for instance, the Law of Excluded Middle (LEM) p ∨ ¬p is no longer a theorem. My question: aside from the logic formal perspective, is IPL supposed to model/address some specific "kind of world" ? Thanks.
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...

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