the number of vertices and number of edges for the following special graphs (Fil
ID: 3195316 • Letter: T
Question
the number of vertices and number of edges for the following special graphs (Fill in final result instead of formula): Find vertices and edges in the complete graph K100- 1. There are 2. There are vertices and edges in the cycle Cgg 3. There 4. There are vertices and 99- vertices and edges in the wheel W9s- are edges in the complete bipartite graph K10098. 5. 6. The complete graph with the smallest number of edges has vertices and edges in the complete graph Q There are vertices and edges 7. The cycle with the smallest number of edges has vertices and edges 8. The wheel with the smallest number of edges has vertices and edges 9. The complete bipartite graph with the smallest number of edges has vertices and edges. 10. The n-dimensional hypercube with the smallest number of edges has vertices and edges.Explanation / Answer
1)
A complete graph with n vertices has n (n-1)/2
complete graph K100 :
edges, n=100
vertices = (100*99)/2 = 50*99 = 4950
2)
The cycle graph with n vertices is called Cn. The number of vertices in Cn equals the number of edges.
In C99 , there are 99 edges and 99 vertices
3)
in wheel, W98 vertices =n = 98
edges = 2(n-1) = 2 *97 = 194
4) complete bipartite graph K100,98:
vertices = 100+98 = 198
edges = 100*98 = 9800
5) in Hypercube Q7 :
vertices = 27 = 128
edges = 26 * 7 = 448
6) A complete graph with smallest number of edges has 2 vertices and 1 edge.
7)A coplete cycle graph has 3 vertices 3 edge.
8) whell with smallest number of edges has 4 vertices and 6 edges.
9) The complete bipartite graph with smallest number of edges has 2 vertices and 1 edge.
10) n dimentional hypercube with smallest number of edges has
3-dimentional: 8 vertices and 12 edges
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