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...
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 the edges between those vertices represent roads. And suppose that you want to start traveling from town A, pass through each town exactly once, and then end at town F. List all the different paths that you could take Hin: For instance, one of the paths is A, B, C, E, D, F. (These...
Answer all the BLANKS from A to N please.
7. For the graph shown below at the bottom, answer the following questions a) Is the graph directed or undirected? b) What is the deg ()? c) Is the graph connected or unconnected? If it is not connected, give an example of why not d) ls the graph below an example of a wheel? e) Any multiple edges? 0 What is the deg'(E)? ) What is the deg (B)? h) Is...
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...
Question 1: Given an undirected connected graph so that every edge belongs to at least one simple cycle (a cycle is simple if be vertex appears more than once). Show that we can give a direction to every edge so that the graph will be strongly connected. Question 2: Given a graph G(V, E) a set I is an independent set if for every uv el, u #v, uv & E. A Matching is a collection of edges {ei} so...
Please answer question 2. Introduction to Trees
Thank you
1. Graphs (11 points) (1) (3 points) How many strongly connected components are in the three graphs below? List the vertices associated with each one. 00 (2) (4 points) For the graph G5: (a) (0.5 points) Specify the set of vertices V. (b) (0.5 points) Specify the set of edges E. (c) (1 point) Give the degree for each vertex. (d) (1 point) Give the adjacency matrix representation for this graph....
8, (10 pts) Show that given a directed graph G = (V,E) already stored in adjacency matrix form, determining if there is a vertex with in-degree n - 1 and out-degree 0 can be done in O(n) time where n is the number of vertices in V.
8, (10 pts) Show that given a directed graph G = (V,E) already stored in adjacency matrix form, determining if there is a vertex with in-degree n - 1 and out-degree 0 can...
Graph Question
D Question 1 2 pts Which Graph Algorithm (as described in lecture) relies on a Priority Queue to give it maximum efficiency? Prim's Algorithm ⓔ Dijkstra's Algorithm Kuemmel-Deppeler Algorithm Topological Ordering Algorithm Kruskal's Algorithm D Question 7 2 pts At the beginning of the Dijkstra's Algorithm, which of the following must be done? Select all correct choices. set all total weights to O mark all vertices as unvisited O sort all edges set all predecessors to null
D...
1. Figure 1 shows the contents of Δ5 and 115, the final distance and path matrices after the execution of the Floyd-Warshall all-pairs shortest path algorithm on a weighted directed graph D 0 4 16 18 1 10 0 22 24 7 Δ5-115502 115-123ф32 50 40 35 0 20 30 20 15 17 0 Figure 1: Distance(Δ) and Path(11) Matrices (a) Give π(2, 1), the full shortest path from vertex 2 to vertex 1 , as a sequence of vertices,...
(5 marks) a. The pseudo-code for breadth-first search, modified slightly from Drozdek,1 is as follows: void breadthFirstSearch (vertex w) for all vertices u num (u) 0 null edges i=1; num (w) i++ enqueue (w) while queue is not empty dequeue ( V= for all vertices u adjacent to v if num(u) is 0 num (u) = i++; enqueue (u) attach edge (vu) to edges; output edges; Now consider the following graph. Give the breadth-first traversal of the graph, starting from...