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- 7. a) How many different paths of length 2 are there in the undirected graph G in Fig. 11.43? b) Let G = (V, E) be a loop-free undirected graph, where V= {U, v2. ..., v) and deg(v,) = d,, for all I sisn. How many different paths of length 2 are there in G? Figure 11.43Let G = (V, E) be a connected graph with a bridge e = uv. Prove that there exist two disjoint sets of vertices U,W whose union is V where any path of G from vertices of U to vertices of W contains e.3 and 4
- 7. Triangle JKL with vertices J(-3, 1), K(–1, 4), and L(6, –5) | -5 5. -53.7 The complete tripartite graph K, consists of three sets of vertices (of sizes r, s and 1), with an edge joining two vertices if and only if they lie in different sets. Draw the graphs K2.2.2 and K3,3,2 and find the number of edges of K3,4,5-Let x and y be two adjacent vertices in the complete bipartite graph Kn,n, n ≥ 3.Find the number of x-y paths of length 2, of length 3, and of length 4.
- Which one of the following is not a trail 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,w},{w,v},{v,x},(x,z},{z,y}} {{x,w),{w,v},{v,x},{x,w},{w,y}} {{x,v},{v,z},{z,w},{w,x},{x,y}} {{x,v},{v,w},{w,z},{z,x},{x,y}}For which of the following does there exist a simple graph G = - (V, E) satisfying the specified conditions? Select one: O A. It has 7 vertices, 10 edges, and more than two components. B. It has 8 vertices, 8 edges, and no cycles. O C. It has 6 vertices, 11 edges, and more than one component. O D. It is connected and has 10 edges, 5 vertices and fewer than 6 cycles. O E. It has 3 components, 20 vertices and 16 edges.If u and v are vertices of a connected graph G, then d(u, v) is the length of a shortest path in G joining u and v. We call d(u, v) the distance from u to vShow that for any three vertices d(u, v) + d(v, w ) > = d(u, w)