What is the chromatic number of n-cube?

What is the chromatic number of n-cube?

The n-cube is bipartite, so its chromatic number is 2. If we label the vertices canonically with vectors in , then we can partition the vertices into those with an even number of 1’s and those with an odd number of 1’s.

How many edges are in a n-cube?

12 edges
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.

What is the chromatic number of the n dimensional hypercube?

In graph theory, the hypercube graph Qn is the graph formed from the vertices and edges of an n-dimensional hypercube. For instance, the cubical graph Q3 is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube….

Hypercube graph
Diameter n
Girth 4 if n ≥ 2
Automorphisms n! 2n
Chromatic number 2

What is the chromatic number for Q2?

Chromatic Number of Q2 11.2 (D. R. Woodall, [Woo1]) χ(Q2) = 2.

What is n-cube graph?

Abstract. The n-cube is characterized as a connected regular graph in which for any three vertices u, v, and w there is a unique vertex that lies simultaneously on a shortest (u, v)-path, a shortest (v, w)-path, and a shortest (w, u)-path.

What is meant by chromatic number?

The chromatic number of a graph is the smallest number of colors needed to color the vertices of so that no two adjacent vertices share the same color (Skiena 1990, p. 210), i.e., the smallest value of. possible to obtain a k-coloring.

What is the chromatic number of a tree with n vertices?

Trees- A Tree is a special type of connected graph in which there are no circuits. Every tree is a bipartite graph. So, chromatic number of a tree with any number of vertices = 2.

What is the chromatic number of K2 3?

The chromatic number of K2,3 is 2.

How many chromatic numbers are there?

The chromatic number, χ(Sk),of a surface Sk is the largest χ(G) such that G can be imbedded in Sk. We prove that six colors will suffice for every planar graph.

Does a cube have 24 edges?

Consider first a three-dimensional cube. At each vertex there are 3 edges, and since the cube has 8 vertices, we can multiply these numbers to give 24 edges in all.

How many vertices does N cube have?

8 vertices
Vertices of cube There are 8 vertices in a cube.