need help filling in the code def prim(G): Use Prim's algorithm to find a MST for the graph G … # Initialize tree T with a single vertex and no edges v = next(iter( )) # while the vertex set of T is smaller than the v+tex set of G, # (i.e. while the vertex set of T is a proper subset of the vertex set of G), find the edge e with minimum weight so that # Tte is...
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...
Let G = (V;E) be an undirected and unweighted graph. Let S be a subset of the vertices. The graph induced on S, denoted G[S] is a graph that has vertex set S and an edge between two vertices u, v that is an element of S provided that {u,v} is an edge of G. A subset K of V is called a killer set of G if the deletion of K kills all the edges of G, that is...
* Exercise 1: Let G be the graph with vertex set V(G) = Zi,-{0,-, that two vertices x, y E V(G) are connected by an edge if and only if ,10) and such ryt5 mod 11 or xEy t7 mod 11 1. Draw the graph G. 2. Show that the graph G is Eulerian, i.e., it has a closed trail containing all its edges
Problem 8. (2+4+4 points each) A bipartite graph G = (V. E) is a graph whose vertices can be partitioned into two (disjoint) sets V1 and V2, such that every edge joins a vertex in V1 with a vertex in V2. This means no edges are within V1 or V2 (or symbolically: Vu, v E V1. {u, u} &E and Vu, v E V2.{u,v} &E). 8(a) Show that the complete graph K, is a bipartite graph. 8(b) Prove that no...
Let G = (V, E, W) be a connected weighted graph where each edge e has an associated non-negative weight w(e). We call a subset of edges F subset of E unseparating if the graph G' = (V, E\F) is connected. This means that if you remove all of the edges F from the original edge set, this new graph is still connected. For a set of edges E' subset of E the weight of the set is just the...
Viterbi algorithm We can use dynamic programming on a directed graph G = (V, E) for speech recognition. Each edge (u, v) in E is labeled with a sound s(u, v) from a finite set S of sounds. The labeled graph is a formal model of a person speaking a restricted language. Each path in the graph starting from a distinguished vertex v0 in V corresponds to a possible sequence of sounds produced by the model. The label of a...
Consider the following weighted, directed graph G. There are 7 vertices and 10 edges. The edge list E is as follows:The Bellman-Ford algorithm makes |V|-1 = 7-1 = 6 passes through the edge list E. Each pass relaxes the edges in the order they appear in the edge list. As with Dijkstra's algorithm, we record the current best known cost D[V] to reach each vertex V from the start vertex S. Initially D[A]=0 and D[V]=+oo for all the other vertices...
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...
Hi, I could use some help for this problem for my discrete math class. Thanks! 18. Consider the graph G = (V, E) with vertex set V = {a, b, c, d, e, f, g} and edge set E = {ab, ac, af, bg, ca, ce) (here we're using some shorthand notation where, for instance, ab is an edge between a and b). (a) (G1) Draw a representation of G. (b) (G2) Is G isomorphic to the graph H -(W,F)...