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A cube is bipartite platonic graph. You can represent it as platonic by drawing one square inside another and connecting respective edges. Start from any vertex, name it A, color it black. Color the adjacent vertices red and name them B, C, D. Take one of the red vertices (i,e, B, C, D)and all adjacent vertices should be black... and so on. You will be able to get cube with no edges between two vertices of same color. This shows it should be bipartite as well as we used only two color to represent graph. Furthermore, put vertices of black and red color in two partitions and connect them with same edges as in the previous graph. Since, there is no edge between two vertices of same color this is bipartite graph as required.
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Which platonic solids are prisms?
A cube is the only platonic solid which is a prism.
Is a cylinder a platonic solid?
No. All the faces of a Platonic solid are identical regular polygons.
Where does the name platonic solid come from?
The Name Platonic solid Comes from Plato the second main reseacher of the five solids. Pythagoras was the one discovered the platonic solids
The number of Platonic solids?
There are 5 platonic solids. They are: Tetrahedron, Octahedron, Icosahedron, Cube, and Dodecahedron
What does each platonic solid represent?
Platonic solids are 3D shapes formed using only regular shapes. Only 1 type of regular shape is used to make a platonic solid. Platonic solids are the simplest and purest form of 3D shapes.
Is tree a bipartite graph?
Yes. A graph is bipartite if it contains no odd cycles. Since a tree contains no cycles at all, it is bipartite.
Is every tree a bipartite graph?
Yes, every tree ia a bipartite graph (just see wikipedia).
What is the automorphism group of a complete bipartite graph?
The automorphism group of a complete bipartite graph K_n,n is (S_n x S_n) semidirect Z_2.
What is a bigraph?
A bigraph is another term for a bipartite graph - in mathematics, a graph whose vertices can be divided into two disjoint sets.
What is a biclique?
A biclique is a term used in graph theory for a special kind of bipartite graph where every vertex of the first set is connected to every vertex of the second set.
Show that the star graph is the only bipartiate graph which is a tree?
A star graph, call it S_k is a complete bipartite graph with one vertex in the center and k vertices around the leaves. To be a tree a graph on n vertices must be connected and have n-1 edges. We could also say it is connected and has no cycles. Now a star graph, say S_4 has 3 edges and 4 vertices and is clearly connected. It is a tree. This would be true for any S_k since they all have k vertices and k-1 edges. And Now think of K_1,k as a complete bipartite graph. We have one internal vertex and k vertices around the leaves. This gives us k+1 vertices and k edges total so it is a tree. So one way is clear. Now we would need to show that any bipartite graph other than S_1,k cannot be a tree. If we look at K_2,k which is a bipartite graph with 2 vertices on one side and k on the other,can this be a tree?
Which figure has faces that are congruent to its bases?
A Platonic solid.A Platonic solid.A Platonic solid.A Platonic solid.
Meaning of bipartite?
having two parts.
What was a bipartite government?
A government consisting of two parts
What are bipartite and tripartite bodies in dispute settlement?
Bipartite bodies in a dispute settlement is an agreement between two parties. Tripartitie bodies is an agreement between three parties involved in a settlement.
Prove that every tree with two or more vertices is bichromatic?
Prove that the maximum vertex connectivity one can achieve with a graph G on n. 01. Define a bipartite graph. Prove that a graph is bipartite if and only if it contains no circuit of odd lengths. Define a cut-vertex. Prove that every connected graph with three or more vertices has at least two vertices that are not cut vertices. Prove that a connected planar graph with n vertices and e edges has e - n + 2 regions. 02. 03. 04. Define Euler graph. Prove that a connected graph G is an Euler graph if and only if all vertices of G are of even degree. Prove that every tree with two or more vertices is 2-chromatic. 05. 06. 07. Draw the two Kuratowski's graphs and state the properties common to these graphs. Define a Tree and prove that there is a unique path between every pair of vertices in a tree. If B is a circuit matrix of a connected graph G with e edge arid n vertices, prove that rank of B=e-n+1. 08. 09.
What is platonic digit?
Not aware of anything such as a Platonic digit.
