question 1 and 2 please, thank you.
1. In the following graph, suppose that the vertices A, B, C, D, E, and F represent towns, and th...
Bonus 1 A walk in a graph G is a sequence of vertices V1, V2, ..., Uk such that {Vi, Vi+1} is an edge of G. Informally, a walk is a sequence of vertices where each step is taken along an edge. Note that a walk may visit the same vertex more than once. A closed walk is a walk where the first and last vertex are equal, i.e. v1 = Uk. The length of a walk is the number...
a. b. c. d. e. What are the vertices? Is this graph connected? What is the degree of vertex C? Edge FE is adjacent to which edges? Does this graph have any bridges? Answer the following questions based on the graph below. 1w a. b. c. d. What are the vertices? What is the degree of vertex u? What is the degree of vertex s? What is one circuit in the graph?
Let G (V, E) be a directed graph with n vertices and m edges. It is known that in dfsTrace of G the function dfs is called n times, once for each vertex It is also seen that dfs contains a loop whose body gets executed while visiting v once for each vertex w adjacent to v; that is the body gets executed once for each edge (v, w). In the worst case there are n adjacent vertices. What do...
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...
Shortest paths Consider a directed graph with vertices fa, b, c, d, e, f and adjacency list representation belovw (with edge weights in parentheses): a: b(4), f(2) e: a(6), b(3), d(7) d: a(6), e(2) e: d(5) f: d(2), e(3) (i) Find three shortest paths from c to e. (ii) Which of these paths could have been found by Dijkstra's shortest path algorithm? (Give a convincing explanation by referring to the main steps of the algorithm.)
Let G -(V, E) be a graph. The complementary graph G of G has vertex set V. Two vertices are adjacent in G if and only if they are not adjacent in G. (a) For each of the following graphs, describe its complementary graph: (i) Km,.ni (i) W Are the resulting graphs connected? Justify your answers. (b) Describe the graph GUG. (c) If G is a simple graph with 15 edges and G has 13 edges, how many vertices does...
Below is the Graph file that needs to be modified(using Python3) : #!/usr/bin/python3 # Simple Vertex class class Vertex: """ Lightweight vertex structure for a graph. Vertices can have the following labels: UNEXPLORED VISITED Assuming the element of a vertex is string type """ __slots__ = '_element', '_label' def __init__(self, element, label="UNEXPLORED"): """ Constructor. """ self._element = element self._label = label def element(self): """ Return element associated with this vertex. """ return self._element def getLabel(self): """ Get label assigned to...
(a) Sketch a 2D vertex-edge graph of the square pyramid shown below. Euler's formula: v+f=e+2 (b) The square pyramid has 5 faces and 5 vertices. How many edges does it have? (c) Label each geometric solid as possible or impossible. 8 vertices, 14 edges, 6 faces 7 vertices, 12 edges, 7 faces
only (i) Practice Problems Problem 11.3. Which of the items below are simple-graph properties preserved under isomor phism? (a) The vertices can be numbered 1 through 7 (b) There is a cycle that includes all the vertices. (c) There are two degree 8 vertices (d) Two edges are of equal length. (e) No matter which edge is removed, there is a path between any two vertices (10) There are two cycles that do not share any vertices (g) One vertex...
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...