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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 every tree a bipartite graph?
No, not every tree is a bipartite graph. A tree is a bipartite graph if and only if it is a path graph with an even number of nodes.
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.
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.
Meaning of bipartite?
"Bipartite" refers to a graph or network that can be divided into two sets of vertices such that all edges connect vertices from one set to the other, with no edges within the same set. A bipartite graph is also known as a bigraph.
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.
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.
What is platonic digit?
Not aware of anything such as a Platonic digit.
How many platonic solids are their?
There (not their) are 5 platonic solids.
