Prove that all eigenvalues of a graph G are zero if and only if G is...

Question

Question

Prove that all eigenvalues of a graph G are zero if and only if G is a null graph.

Answer 1

Answer #1

Please like if u helps you ?

Gare Se u show that an eigen values y a values g a graph Berw off G is null graph is the nell graph, then its adsency matrix

Answer 2

Similar Homework Help Questions

Prove the Theorem: Theorem: A graph G is a Cayley graph if and only if Aut(G)...

Prove the Theorem: Theorem: A graph G is a Cayley graph if and only if Aut(G) contains a subgroup that acts reg- ularly on G Theorem: A graph G is a Cayley graph if and only if Aut(G) contains a subgroup that acts reg- ularly on G
P9.6.3 Prove that a connected undirected graph G is bipartite if and only if there are no edges b...

P9.6.3 Prove that a connected undirected graph G is bipartite if and only if there are no edges between nodes at the same level in any BFS tree for G. (An undirected graph is defined to be bipartite if its nodes can be divided into two sets X and Y such that all edges have one endpoint in X and the other in Y.) P9.6.3 Prove that a connected undirected graph G is bipartite if and only if there are...
Prove: An edge e of a graph G is a cut-edge if and only if e...

Prove: An edge e of a graph G is a cut-edge if and only if e is not part of any circuit in G.

(3) Prove that for a bipartite graph G on n vertices, we have a(G)- n/2 if and only if G has a pe...

Please answer the question and write legibly (3) Prove that for a bipartite graph G on n vertices, we have a(G)- n/2 if and only if G has a perfect matching. (Recall that α(G) is the maximum size among the independent subsets of G.) (3) Prove that for a bipartite graph G on n vertices, we have a(G)- n/2 if and only if G has a perfect matching. (Recall that α(G) is the maximum size among the independent subsets of...
Suppose that A is diagonalizable and all eigenvalues of A are positive real numbers. Prove that...

Suppose that A is diagonalizable and all eigenvalues of A are positive real numbers. Prove that det (A) > 0. (1 point) Suppose that A is diagonalizable and all eigenvalues of A are positive real numbers. Prove that det(A) > 0. Proof: , where the diagonal entries of the diagonal matrix D are Because A is diagonalizable, there is an invertible matrix P such that eigenvalues 11, 12,...,n of A. Since = det(A), and 11 > 0,..., n > 0,...
Let G be a graph and let µ(G) be the Mycielskian of the graph. Prove the...

Let G be a graph and let µ(G) be the Mycielskian of the graph. Prove the following: ω(µ(G)) = ω(G), where ω(G) is the clique number of the graph, G.

Linear Algebra 4. Prove that the eigenvalues of A and AT are identical. 5. Prove that...

Linear Algebra 4. Prove that the eigenvalues of A and AT are identical. 5. Prove that the eigenvalues of a diagonal matrix are equal to the diagonal elements. 6. Consider the matrix ompute the eigenvalues and eigenvectors of A, A-,
A.) Prove that if some graph G is an Eulerian graph, the L(G) {the line graph of G} is also Euler...

A.) Prove that if some graph G is an Eulerian graph, the L(G) {the line graph of G} is also Eulerian. B.) Find a connected non-Eulerian graph for which the line graph is Eulerian.
Assume all matricies are Mmxm(R) unless otherwise specified. 1. (1 point) Prove or disprove that the...

Assume all matricies are Mmxm(R) unless otherwise specified. 1. (1 point) Prove or disprove that the eigenvalues of A and AT are the same. 2. (2 points) Let A be a matrix with m distinct, non-zero, eigenvalues. Prove that the eigenvectors of A are linearly independent and span R”. Note that this means in this case) that the eigenvectors are distinct and form a base of the space. 3. (1 point) Given that is an eigenvalue of A associated with...

Please do number 2 Assume all matricies are Mmxm(R) unless otherwise specified. 1. (1 point) Prove...

Please do number 2 Assume all matricies are Mmxm(R) unless otherwise specified. 1. (1 point) Prove or disprove that the eigenvalues of A and AT are the same. 2. (2 points) Let A be a matrix with m distinct, non-zero, eigenvalues. Prove that the eigenvectors of A are linearly independent and span R”. Note that this means in this case) that the eigenvectors are distinct and form a base of the space. 3. (1 point) Given that is an eigenvalue...