Prove that if a graph has an Eulerian path, then the number of odd ...
Oct 14, 2023 · Now, let's use these properties to prove the statement. If a graph has an Eulerian path, there must be exactly two vertices with odd degrees (the starting and ending vertices) …
discrete mathematics - Confusion about euler path,trail,circuit ...
Jul 20, 2017 · What's the difference between a euler trail, path,circuit,cycle and a regular trail,path,circuit,cycle since edges cannot repeat for all of them anyway? And can vertices be …
graph theory - Prove that $L (G)$ is Eulerian if $G$ is Eulerian ...
May 22, 2021 · Prove that $L (G)$ is Eulerian if $G$ is Eulerian. My idea is: If $G$ is Eulerian, then all vertices are of even degree; in other words, an even number of edges are incident on …
For which n is K$_n$ Eulerian? - Mathematics Stack Exchange
For my answer so far, I've got something along the lines of: "K$_n$ is a complete graph if each vertex is connected to every other vertex by one edge. Therefore if n is even, it has n-1 edges …
Is Eulerian graph necessarily connected? - Mathematics Stack …
Oct 3, 2020 · The reason I ask is because I came across this question: Graph and its line Graph that both contain Eulerian circuits And the solution seems to assume that the graph is …
Eulerian walk proof: If a connected graph has exactly two nodes …
Feb 26, 2012 · Prove that: If a connected graph has exactly two nodes with odd degree, then it has an Eulerian walk. Every Eulerian walk must start at one of these and end at the other one. …
graph theory - Prove that $G$ is Eulerian if and only if every block …
May 22, 2021 · Proof: If every block is eulerian then degree of each vertex of the block should be even (even the separating vertex). For any separating vertex in $G$, say $u$, its degree in all …
eulerian path - Proving the theorem of graph theory
Jun 19, 2014 · I want to know the proof of the condition of a Euler walk or tour in a directed graph. I googled a lot about it from MIT courseware to some other YouTube channels but I couldn't …
Euler path for directed graph? - Mathematics Stack Exchange
How do we find Euler path for directed graphs? I don't seem to get the algorithm below! Algorithm To find the Euclidean cycle in a digraph (enumerate the edges in the cycle), using a greedy …
discrete mathematics - What are the necessary and sufficient …
The definition says "A directed graph has an eulerian path if and only if it is connected and each vertex except 2 have the same in-degree as out-degree, and one of those 2 vertices has out …