[Graph Theory] How do you solve a) and b)?For a), would the maximum number of vertices be 202 if you made a cycle graph where every pair of vertices has at most one edge? How would you calculate the minimum number of vertices?For b), is G self-complementary? Definition 5.4.15. Graph Complement. Let G = (V,E) be a simple graph.We define its complement G to be the graph on the same vertex set V(G), andwith edge setE' = {(u, v) E V × V : (u, v) £ E},that is, (u, v) is an edge in G if and only if it was not an edge in G.Example 5.4.16. A Graph and its Complement. A graph G (red) and itscomplement G (blue) are shown below.53 63 631212GG A connected simple graph G has 202 edges.(a) Determine the minimum and maximum number of vertices it can have. Explain your reasoning.(b) Can G be self-complementary? Why or why not?

Let G be a connected graph with 202.

Answered: A connected simple graph G has 202…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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[Graph Theory] How do you solve a) and b)?

For a), would the maximum number of vertices be 202 if you made a cycle graph where every pair of vertices has at most one edge? How would you calculate the minimum number of vertices?

For b), is G self-complementary?

Definition 5.4.15. Graph Complement. Let G = (V,E) be a simple graph.
We define its complement G to be the graph on the same vertex set V(G), and
with edge set
E' = {(u, v) E V × V : (u, v) £ E},
that is, (u, v) is an edge in G if and only if it was not an edge in G.
Example 5.4.16. A Graph and its Complement. A graph G (red) and its
complement G (blue) are shown below.
5
3 6
3 6
3
1
2
1
2
G
G

A connected simple graph G has 202 edges.
(a) Determine the minimum and maximum number of vertices it can have. Explain your reasoning.
(b) Can G be self-complementary? Why or why not?

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