Why does a 3-regular planar graph of diameter 3 have at most 12 …
Sep 18, 2023 · 5 Today, I saw an interesting exercise on page 224 of the West textbook "Introduction to Graph Theory". 6.1.15. Construct a 3-regular planar graph of diameter 3 with 12 vertices. (Comment: …
How to find the angle created when joining two vertices of four ...
Nov 3, 2025 · The text of the problem, taken from the picture: Optional challenge (required to understand it once we go over it): 4 squares are drawn and two segments are drawn between …
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. …
How to sort vertices of a polygon in counter clockwise order?
16 How to sort vertices of a polygon in counter clockwise order? I want to create a function (algorithm) which compares two vectors $\vec v$ and $\vec u$ which are vertices in a polygon. It should choose …
Prove the existence of a graph of 15 vertices with some vertices degree ...
4 this is the exercise: If possible draw a graph with 15 vertices having 3 vertices with degree 4; 4 vertices with degree 3; 6 vertices with degree 2; 0 vertices with degree greater than the ones of the …
Drawing all non-isomorphic trees with $n = 5$ vertices.
Jul 29, 2017 · I followed the instructions in this question to create the trees for n = 1, n = 2, n = 3, n = 4, and n = 5. Note that I created rooted trees instead of free trees because it was easier. You can get...
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 …
Eulerian paths visiting at most 2 vertices and odd degree edges
Oct 1, 2020 · I have 20 vertices (If we count u0 until u19 is 20 vertices).Its not Euler cause it has all those u1,u2,u3,u9,u14,u16,u17,u18 all those vertices have 3 edges each one that makes not Euler. …
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 …
How to calculate the number of possible connected simple graphs with …
For Kn, there will be n vertices and (n (n-1))/2 edges. To determine how many subsets of edges a Kn graph will produce, consider the powerset as Brian M. Scott stated in a previous comment. If S is a …