polyhedra - Polyhedron with least number of vertices whose …
Dec 6, 2025 · The least number of vertices that a polyhedron can have, such that its diagonal faces enclose an interior solid region? Note: "interior" means the solid does not intersect the …
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 …
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.
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 …
How many nonisomorphic directed simple graphs are there with …
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 …
Proving that the number of vertices of odd degree in any graph G …
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 …
geometry - How many verticies, edges and faces (cells) does an nd ...
Mar 19, 2021 · So I guess a 1d hypercube is a line segment. It has 2 verticies and 1 edge. Not sure how many faces it has? A 2d hypercube is a square. It has 4 verticies and 4 edges. Again …
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 …
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 $4$ …
Show that a connected graph on $n$ vertices is a tree if and only …
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: