a) Since 4 vertices are pair-wise disjoint, between those vertices there is no edge.
And any other vertex should have an edge to atleast one of the vertex from this set or else pair-wise
disjoint vertices becomes 5.
So, atleast these 4 vertices are needed for minimum vertex cover.
b) And since they don't have any edge among them, By selecting all other 8 vertices we can cover all the
edges.
Hence, minimum cover can be atmost 8.
#2. Answer with explanations. Graph G with 12 vertices has 4 pair-wise nonadjacent vertices. What could...
#2. Answer with explanations. Graph G with 12 vertices has 4 pair-wise nonadjacent vertices. What could be said about its minimum vertex cover of G? It has... Yes No Impossible to determine a) at least 4 vertices because Yes No Impossible to determine b) at most 8 vertices because
#2. Answer with explanations. Graph G with 12 vertices has 4 pair-wise nonadjacent vertices. What could be said about its minimum vertex cover of G? It has... Yes No Impossible to determine a) at least 4 vertices because Yes No Impossible to determine b) at most 8 vertices because
A graph (G) with 12 Vertices has 4 PAIR-WISE non-Adjacent Vertices, What could be said for its Minimum Vertex Cover of G? at Least 4 vertices (Yes, No, Impossible to determine?) b) at Most 8 vertices (Yes, No, Impossible to determine?)
Draw a Graph with 12 vertices which has 4 pair-wise nonadjacent vertices.
Let G be a non-Hamiltonian, connected graph. For every pair of nonadjacent vertices u and v, 8(u) +8()2 k, for some k> O. Show that G contains a path of length k.
Let G be a non-Hamiltonian, connected graph. For every pair of nonadjacent vertices u and v, 8(u) +8()2 k, for some k> O. Show that G contains a path of length k.
PLEASE HELP Let G is a graph with 2n vertices and n^2 edges. An amicable pair of vertices is an unordered pair (u, v), such that dist(u, v) = 2. Prove that G has at least n(n − 1) amicable pairs of vertices.
Recall the definition of the degree of a vertex in a graph. a)
Suppose a graph has 7 vertices, each of degree 2 or 3. Is the graph
necessarily connected ?
b) Now the graph has 7 vertices, each degree 3 or 4. Is it
necessarily connected?
My professor gave an example in class. He said triangle and a
square are graph which are not connected yet each vertex has degree
2.
(Paul Zeitz, The Art and Craft of Problem...
please show work as well as answer
Complete. Ri. Triangle ABC has vertices A(2,0), B(4,-1), and C(1,-3). Graph the figure and its image after a clockwise rotation of 180° about vertex A. Give the coordinates of the vertices for triangle A'B'C.
Complete. Ri. Triangle ABC has vertices A(2,0), B(4,-1), and C(1,-3). Graph the figure and its image after a clockwise rotation of 180° about vertex A. Give the coordinates of the vertices for triangle A'B'C.
Say that we have an undirected graph G(V, E) and a pair of vertices s, t and a vertex v that we call a a desired middle vertex . We wish to find out if there exists a simple path (every vertex appears at most once) from s to t that goes via v. Create a flow network by making v a source. Add a new vertex Z as a sink. Join s, t with two directed edges of capacity...
Draw a simple undirected graph G that has 12 vertices, 18 edges, and 3 connected components. Why would it be impossible to draw G with 3 connected components if G has 66 edges?