Look up the definition of a biconnected undirected graph on Wikipedia. Give a one sentence definition based on induced sub-graphs. Start your definition with “An undirected graph G = (V, E) is biconnected, if . . . ” (b) For a directed graph G = (V, E), its underlying undirected graph is obtained by replacing every directed edge (u, v) with an undirected one . (If (u, v) and (v, u) are both in E, then the underlying undirected graph still contains only one edge .) Give a strongly connected directed graph such that its underlying undirected graph is not biconnected. Question 2 (a) Look up the definition of a biconnected undirected graph on Wikipedia. Give a one sentence definition based on induced sub-graphs. Start your definition with "An undirected graph G (V, E) is biconnected, if..." b) For a directed graph G-(V,E), its underlying undirected graph is obtained by replacing every directed edge (u, v) with an undirected one 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... Problem4 Let G = (V. E) be an undirected, connected graph with weight function w : E → R. Furthermore, suppose that E 2... Problem4 Let G = (V. E) be an undirected, connected graph with weight function w : E → R. Furthermore, suppose that E 2 |V and that all edge weights are distinct. Prove that the MST of G is unique (that is, that there is only one minimum spanning tree of G). Problem4 Let G = (V. E) be an undirected, connected graph with weight function w : E → R. Furthermore, suppose that E 2 |V and that all... Question 1: Given an undirected connected graph so that every edge belongs to at least one... 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 so... 6. Prove that the following graphs are connected: (a) The 3 vertex cycle: (b) The following 4 vertex graph: (c) K 7. An edge e of a connected graph G is called a cut edge if the graph G obtained by d... 6. Prove that the following graphs are connected: (a) The 3 vertex cycle: (b) The following 4 vertex graph: (c) K 7. An edge e of a connected graph G is called a cut edge if the graph G obtained by deleting that edge (V(G) V(G) and E(G) E(G) \<ej) is not connected. Prove that if G1 and G2 are connected simple graphs which are isomorphic and if G1 has a cut edge, then G2 also has a cut edge.... MST For an undirected graph G = (V, E) with weights w(e) > 0 for each edge e ∈ E, you are given a MST T. Unfortunately one of the edges e* = (u, z) which is in the MST T is deleted from the graph G... MST For an undirected graph G = (V, E) with weights w(e) > 0 for each edge e ∈ E, you are given a MST T. Unfortunately one of the edges e* = (u, z) which is in the MST T is deleted from the graph G (no other edges change). Give an algorithm to build a MST for the new graph. Your algorithm should start from T. Note: G is connected, and G − e* is also connected. Explain... NAME . You are given a strongly connected directed graph G (V, E) with positive edge... NAME . You are given a strongly connected directed graph G (V, E) with positive edge weights along with a particular node vo E V. Give an efficient algorithm for finding shortest paths between all pairs of nodes, with the one restriction that these paths must all pass through v (8 points) Ems B-1 Graph coloring Given an undirected graph G (V. E), a k-coloring of G is a function c : V ... ems B-1 Graph coloring Given an undirected graph G (V. E), a k-coloring of G is a function c : V - (0. I. . . . .k-1) such that c (11)关c (v) for every edge (u, v) E E. In other words, the numbers 0.1,... k 1 represent the k colors, and adjacent vertices different colors. must have c. Let d be the maximum degree of any vertex in a graph G. Prove that we can color G with... Reachability. You are given a connected undirected graph G = (V, E ) as an adjacency... Reachability. You are given a connected undirected graph G = (V, E ) as an adjacency list. The graph G might not be connected. You want to fill-in a two-dimensional array R[,] so that R[u,v] is 1 if there is a path from vertex u to vertex v. If no such path exists, then R[u,v] is 0. From this two-dimensional array, you can determine whether vertex u is reachable from vertex v in O(1) time for any pair of vertices... ems B-1 Graph coloring Given an undirected graph G (V. E), a k-coloring of G is... ems B-1 Graph coloring Given an undirected graph G (V. E), a k-coloring of G is a function c : V - (0. I. . . . .k-1) such that c (11)关c (v) for every edge (u, v) E E. In other words, the numbers 0.1,... k 1 represent the k colors, and adjacent vertices different colors. must have c. Let d be the maximum degree of any vertex in a graph G. Prove that we can color G with... Free Homework Help App Download From Google Play Scan Your Homework to Get Instant Free Answers Need Online Homework Help? Ask a Question Get Answers For Free Most questions answered within 3 hours. Share Your Knowledge Post an Article Post an Answer Post a Question with Answer Earn Money Contribute Homework Answers ($1+ Per Post) Recent Questions Recent Answers Chapter 1 Begin Date: 6/23/2020 12:01:00 AM -- Due Date: 6/29/2020 3:30:00 PM End Date: 8/31/2020... asked 3 minutes ago Label the H on the picture For example: (2H) , (3H) Unknown #4 Additional 13C peak... asked 10 minutes ago Show work so I can understand thanks. 1. 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