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) …

Usually one speaks of adjacent vertices, but of incident edges. Two vertices are called adjacent if they are connected by an edge. Two edges are called incident, if they share a vertex. Also, a …

Jan 14, 2022 · 2 A simple graph $G$ with $n$ vertices in which the sum of degrees of every two non-adjacent vertices is at least $n-1$ has a Hamiltonian path.

I have tried some ways - mainly using induction by removing one of the vertices of the set from the graph, and/or using Menger's theorem to construct the cycle. But I always encounter …

A directed simple graph is a structure consisting of the set of vertices and a binary relation that is irreflexive. For the case of the disconnected graph, the relation is empty, and there is one such …

Dec 11, 2010 · Anyone know of an online tool available for making graphs (as in graph theory - consisting of edges and vertices)? I have about 36 vertices and even more edges that I wish to …

Jan 23, 2015 · To prove that the number of odd vertices in a simple graph is always even, we can use the Handshaking Lemma, which states that the sum of the degrees of all vertices in a …

Here's alternative proof that a connected graph with n vertices and n-1 edges must be a tree modified from yours but without having to rely on the first derivation:

Apr 4, 2025 · The Question: Given a list of the vertices in a platonic solid, is there a way to calculate which vertices are connected by an edge? I know that one could find edges using …

Aug 18, 2021 · In general having three vertices of a parallelogram allows for three possible positions of the fourth vertex, depending on which pair of the three are endpoints of a diagonal …