Which one of the following 4-vertex undirected graphs G=(V,E), where V={a,b,c,d} is loop-free? Assume all edges shown belong to the edge set E for that graph. {{a,b},{b,c},{c,c},{b,d}} {{a,b},{b,c},{a,c},{b,d}} {{a,b},{b,c},{a,a},{b,d}} {{b,b),{b,c},{a,c},{b,d}}

Which one of the following is a path from vertex x to vertex y for the graph G=(V,E), if V={v,w,x,y,z}? Assume all edges shown belong to the edge set E. Group of answer choices   {{x,z},{z,w},{w,v},{v,y}} {{x,z},{z,w},{w,z},{z,y}} {{x,w},{w,z},{z,w},{w,y}} {{x,v},{v,w},{w,v},{v,y}}

Write a function in a directed graph represented by adjacency lists that returns true (1) if an edge exists between two provided vertices u and v and false (0) otherwise.

If removing any 3 vertices from a connected graph G keeps it connected then: A- G must be 4-vertex connected B-G must be 3-vertex connected C-The edge connectivity of G must be at least 4 D-The vertex connectivity of G must be at least 4

Consider the following edge-weighted digraph with 8 vertices and 13 edges. V->W weight A->E 1 A->B B->C C->F 4 C->D D->G F->E 39 23 F->B 26 F->A 16 G->F G->C 40 34 H->D 95 H->G 17 Here is a graphical representation of the same edge-weighted digraph: (A) -3---->(B) -39-->(D) 16 95 (E)- -23- (F). 40 (G) (H) Suppose that you run the Bellman-Ford algorithm to compute the shortest paths from H to every other vertex. What is the distTo[] array immediately after the end of three passes of the algorithm (pass 1, 2, and 3)? Each pass consists of relaxing the 13 edges in the order given above. Here is the distTo[] array before the beginning of pass 1: v A B CDE F H. distTo(v] Answer Your answer should be a sequence of 8 integers, separated by whitespace,

Suppose G=(V,E) is a 4-vertex directed graph with V={a,b,c,d} and E = {(a,b), (a,c), (a,d), (c,b), (d,c)}.  What is the in-degree of vertex a? Group of answer choices 0 3 1 2

Consider the following edge-weighted graph with 10 vertices and 17 edges. V-w weight A-B 8. F-A 6. G-B 15 B-F C-B D-C 16 C-G 12 C-H C-I D-I 17 D-E 11 I-E 13 J-E 10 G-F 9. H-G I-H 14 1 I-J Here is a graphical representation of the same edge-weighted graph: (A) -8- (C)------16----- (D)---- --11-----(E) 7|\ 13 10 (F) (G) Give the sequence of edges in the MST in the order that Prim's algorithm adds them to the MST, when starting Prim's algorithm from vertex H. To specify an edge, use its weight.

A graph has the following edge-endpoint function table. Edge Edgepoints {v. v3} e2 {v2 v3} {v3, Va} {va Vs} e4 {v3, Vs} es {v5, Vs) es ez {vs, V7} eg {v, Vs} eg {v2, v;} Based on the preceding table, find the number of edges incident on the designated vertic Number of edges Vertices incident on the vertex V1 V2 V3 VA V5 V6 V7 V8

Please according to the following figure, which are right ? multiple choice

Given a graph G = (V;E) an almost independent set I  V is a generalization of an independent set whereeach vertex u 2 I is connected to at most one other vertex in I but no more. In other words for all u; v 2 Iif (u; v) 2 E then (u; z) =2 E for all z 2 I (equvalently (v; z) =2 E). Note that every independent set is alsoalmost independent. Prove that the problem of  nding whether there exists an almost independent set ofsize k for some k, is NP-complete.