Show that the number of labelled simple graphs with n vertices is 2n(n-1)/2. (By induction way!)

Show that the number of labelled simple graphs with n vertices is 2^n(n-1)/2. (By induction way!)

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Prove the following by induction: 2 + 4 + 6 + …+ 2n = n(n+1) for...

Prove the following by induction: 2 + 4 + 6 + …+ 2n = n(n+1) for all integers n Show all work

Show by induction that for all n natural numbers 0+1+4+9+16+...+ n^2 = n(n+1)(2n+1)/6.

1a. Proof by induction: For every positive integer n, 1•3•5...(2n-1)=(2n)!/(2n•n!). Please explain what the exclamation mark...

1a. Proof by induction: For every positive integer n, 1•3•5...(2n-1)=(2n)!/(2n•n!). Please explain what the exclamation mark means. Thank you for your help! 1b. Proof by induction: For each integer n>=8, there are nonnegative integers a and b such that n=3a+5b

By induction: 1. Prove that Σni=1(2i − 1) = n2 2. Prove thatΣni=1 i2 = n(n+1)(2n+1)...

By induction: 1. Prove that Σni=1(2i − 1) = n2 2. Prove thatΣni=1 i2 = n(n+1)(2n+1) / 6 .

Prove these scenarios by mathematical induction: (1) Prove n2 < 2n for all integers n>4 (2)...

Prove these scenarios by mathematical induction: (1) Prove n2 < 2n for all integers n>4 (2) Prove that a finite set with n elements has 2n subsets (3) Prove that every amount of postage of 12 cents or more can be formed using just 4-cent and 5-cent stamps

2. [6 marks] (Induction) Prove that 21 divides 4n+1 + 5 2n−1 whenever n is a...

2. [6 marks] (Induction) Prove that 21 divides 4n+1 + 5 2n−1 whenever n is a positive integer. HINT: 25 ≡ 4(mod 21)

Let G be a simple undirected graph with n vertices where n is an even number....

Let G be a simple undirected graph with n vertices where n is an even number. Prove that G contains a triangle if it has at least (n^2 / 4) + 1 edges using mathematical induction.

Question 2: A bipartite graph with 2n vertices (namely |V1| = |V2| = n) is d-regular...

Question 2: A bipartite graph with 2n vertices (namely |V1| = |V2| = n) is d-regular if and only if the degree of every vertex in V1 ∪ V2 is exactly d. Show that a d-regular bipartite graph always has a perfect matching (a matching of size n that includes all vertices). ***Remarks: All the graphs here are without self loops and parallel or anti-parallel edges. A network is a directed graph with source s and sink t and capacity...

Show that any graph with n vertices and δ(G) ≥ n/2 + 1 has a triangle.

Use a mathematical induction for Prove a^(2n-1) + b^(2n-1) is divisible by a + b, for...

Use a mathematical induction for Prove a^(2n-1) + b^(2n-1) is divisible by a + b, for n is a positive integer

Subjects