Draw graph with five vertices which has euler circuit and not all degrees of vertices are...
G3: I can determine whether a graph has an Euler trail (or circuit), or a Hamiltonian path (or cycle), and I can clearly explain my reasoning. Answer each question in the space provided below. 1. Draw a simple graph with 7 vertices and 11 edges that has an Euler circuit. Demonstrate the Euler circuit by listing in order the vertices on it. 2. For what pairs (m, n) does the complete bipartite graph, Km,n contain a Hamiltonian cycle? Justify your...
Answer each question in the space provided below. 1. Draw a simple graph with 6 vertices and 10 edges that has an Euler circuit. Demonstrate the Euler circuit by listing in order the vertices on it. 2. For what pairs (m,n) does the complete bipartite graph, Km,n contain an Euler circuit? Justify your answer. (Hint: If you aren't sure, start by drawing several eramples) 3. For which values of n does the complete graph on n vertices, Kn, contain a...
Draw a graph that models the connecting relationships in the floorplan below. The vertices represent the rooms and the edges represent doorways connecting rooms. Vertex F represents the outdoors. Determine whether the graph contains an Euler path or an Euler circuit. If either an Euler path or an Euler circuit exists, find one. B D The graph contains at least one Euler path, but no Euler circuit. An Euler path is DEFBFACFE. The graph contains at least one Euler circuit...
14) For the graph below, if the graph does not have an Euler circuit, explain why not. If it does have an Euler circuit, describe one by a sequence of vertices. 15) For each of the graphs below, determine whether the graph has an Euler trail. If so, find one and give it as a
3. (a) Draw a graph with seven vertices that is 3-chromatic, planar, and without an Euler cycle. (b) Repeat part (a), but now make the graph non-planar.
The graph has an:
A. Neither
B. Euler Circuit
C. Euler path and Euler circuit
D. Euler Path
B A Q E C G
B A Q E C G
Question 3. Draw a graph G = (V. E) on 10 nodes (vertices) with degrees 1.1.1.1.1.1.1.1.5, 5. V = {0, V2.03......}. Is G a tree? Why/why not? (Remember that a tree is a graph which is connected and has no cycles).
A bipartite graph is a graph in which the vertices can be divided into two disjoint nonempty sets A and B such that no two vertices in A are adjacent and no two vertices in B are adjacent. The complete bipartite graph Km,n is a bipartite graph in which |A| = m and |B| = n, and every vertex in A is adjacent to every vertex in B. (a) Sketch K3,2. (b) How many edges does Km,n have? (c) For...
Draw a Graph with 12 vertices which has 4 pair-wise nonadjacent vertices.
Question 5 12 pts Claim: The graph pictured below has an Hamiltonian circuit. O True O False Question 6 12 pts Claim: There exists a graph with 4 vertices with degrees 1, 1, 3, 3. O True O False Question 7 12 pts Claim: The graph pictured below has an Euler circuit. O True O False Question 8 12 pts Claim: The graph pictured below has an Euler circuit. O True O False