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) and all other …
Graph theory: adjacency vs incident - Mathematics Stack Exchange
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 vertex and …
Proving that the number of vertices of odd degree in any graph G is ...
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 graph is twice …
Finding number of edges given vertices and degree sequence?
Feb 15, 2017 · 5 The sum of the vertex degree values is twice the number of edges, because each of the edges has been counted from both ends. In your case $6$ vertices of degree $4$ mean there …
combinatorics - Every $k$ vertices in an $k$ - connected graph are ...
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 problems with …
How many nonisomorphic directed simple graphs are there with $n ...
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 …
discrete mathematics - Simple graph with $G$ with $n$ vertices ...
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.
Online tool for making graphs (vertices and edges)?
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 draw. …
Relationship between vertices and edges in platonic solids
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 edge length or …
Find the 4th vertex of the parallelogram - Mathematics Stack Exchange
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 rather than a side.