Let G = (V,E) be the graph with n vertices and m edges. (i) Define the incidence matrix B = (bij)1≤i≤n.1

Identify the undirected graph represented by the adjacency matrix 1 3 2 3 0 4 2 4 0 b a a b a

Q3) Consider the relation R = {(1,3), (1, 4), (3, 2), (3, 3), (3, 4)} on %3D A = {1,2, 3, 4} a) Find the matrix M, of R. R b) Draw the directed graph of R.

ez V3 V2 V5 V1 V4 (a) Which edges are incident on v,? (b) Which vertices are adjacent to v? (c) Which edges are adjacent to e,?

Find the relation determined by the diagraph and give its matrix.

Can you show that Q is an intensity matrix?

What is the Range of matrix M?

The optimal path for the TSP for a graph represented by the matrix C- (c), is given by the formula g(4, 5) - min (ea+ g(k,S- (k))) kes 2 3 4 6. C- 2 6. 6 429 2 g(2, (3)) -- 2. %24 2. 3. 1.

Draw the graphs from the given adjacency matrix: 1 1 b. 1 2 1 с. 2 3 а. 1 2 1 1 1 1 1 2 1 1 _ 1

(11). Find the adjacency matrix of the following digraph. (a). (b). V4 V1 (12). Find the incidence matrix to the following graph. VI V4 V/3 V3 V₂ V2 V3 O