# Tagged Questions

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### Calculating the central point with minimal average distance to other points

I work at an office with colleagues coming from all over the country. Our office is quite centrally located, but some colleagues have to travel quite a lot further than others. I often wondered how I ...
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### Interactions between geometry and graph theory.

I'm looking for some nice theories or just exercises, with both geometrical aspects and graph theoretics aspects. Example may include for instance the 4-color theorem or Euler characteristics, maybe ...
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### Forming a simple polygon from the extrusion of a polygonal chain

Let's say I have a set of vertices connected by edges to form a polygonal chain. Each vertex may be shared by a number of edges to form various sub-chains. An example is shown below. Each edge has ...
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### Having the number 59 for example find $x$ which $x^2$ is closer but lower to the 59. In this case is 7

I don't know how to name this but this is what I would need. ...
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### Graph theoretic view on manifold triangulations

To make the question (hopefully) clearer, I reformulated it: Some triangulation $T$ of a smooth manifold $M$ is a piecewise linear manifold, because smooth manifolds are topological manifolds. Such a ...
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### Inner angles of an irreducible graph on a sphere

Given an irreducible graph on a ball (a sphere in three dimensions). The inner angles of a triangle, quadrangle and pentagon are smaller than $180^{\circ}$. Could anybody give a proof of this ...
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### Irreducible graph on a sphere

I am trying to grasp an article about the kissing problem in three dimensions (Das Problem der dreizehn Kugeln, by K. Schütte and B.L. van der Waerden). The article deals with irreducible graphs on a ...
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### The shortest path connecting three points

I have 3 points X,Y,Z, lets call them buildings. I need to find the shortest amount of path that connects the 3 buildings, these buildings can be in any sort of shape and any distance from each ...
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### Hypersphere packings from hypercubic graphs?

Consider a $D$-dimensional hypercubic lattice, i.e. a graph $H$ embedded in ${\mathbb R}^D$ where the vertices have integer coordinates $(x_1,...,x_D) \in {\mathbb Z}^D$ and edges are between all ...
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### What is the tutte polynomial

I am really stuck on how to work out the tutte polynomial so any help would be great thanks. G is a graph with 2 vertices, joined by n edges. How to you show what the tutte polynomial is? And what ...
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### How to remove all the parent cycle s in a graphycle 1 => that contain atleast one child cycle?

The following are the points of Cycles:- Cycle1=> {1,2,4,6,7} Cycle2=> {2,3,5,6,7} Cycle3=> {1,3,4,5,6,7} I want to remove the cycle 3 because it contains Cycle 1