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 …

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 …

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 …

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) …

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 …

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 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 …

Aug 30, 2015 · An Eulerian path for the connected graph is also an Eulerian path for the graph with the added edge-free vertices (which clearly add no edges that need to be traversed). …

Oct 7, 2017 · By definition of an Eulerian circuit, we also have to conclude the walk at the same vertex where we started, hence we reach $v_0 = v_k$ again via a different, $k$-th edge $\ {v_ …

In this case however, there is a corresponding theorem for digraphs which says that a digraph (possibly with multiple edges and loops) has an Eulerian circuit if and only if every vertex has …