1. Consider the directed acyclic graph (DAG) D shown below. (a) Write down the adjacency matrix A corresponding to the ordering of the vertices given by alphabetical order: a, b, c, d, e, f, g.

Q2 Let G be the following graph with 5 vertices: 3 (4. 1) Write the adjacency matrix of G 2) Enter your adjacency matrix on Pari (or other software) and use it to calculate the number of paths of length 10 starting at the vertex 1. How many of these paths end at vertex 1? Vertex 2, 3, 4, and 5?

Let A be the adjacency matrix of a complete graph K4.(a) Write down matrix A.(b) How many possible walks with length 2 are there from a (any) node to itself (e.g., from Node 2 to itself) (c) How many possible walks with length 3 are there from a (any) node to the other node (e.g., from Node 2 to Node 3 or Node 1 to Node 4)

FB 5.2 Consider the lexicographically ordered adjacency matrix 0 1 1 1 0 0 1 0 10 0 1 10 1 1 1 A = 10 10 0 0 0 0 10 0 1 0 0 10 1 0 for a graph G with vertex set {a, b, c,d,e,f}. a) Sketch this graph and state the degrees of each of the nodes. b) State, with justification, whether this is a simple graph, or not.

1. Find the adjacency matrix of the given directed multigraph with respect to the vertices listed in alphabetic order.

2. a b C d a) Represent the graph with an adjacency list. b) Represent the graph with an adjacency matrix. c) Represent the graph with an incidence matrix.

3) Let (V, E) be the graph with vertices a, b, c, d, e, f, and g, and edges ab, ac, bc, bd, be, cd, ce, de, af, df, ag, and eg. (a) Draw this graph. (b) Write down this graph's incidence table and its incidence matrix. (c) Write down this graph's adjacency table and its adjacency matrix. (d) Is this graph complete? Justify your answer. (e) Is this graph bipartite? Justify your answer. (f) Is this graph regular? Justify your answer. (g) Does this graph have any regular subgraph? Justify your answer. (h) Give an example of an isomorphism from the graph (V, E) to itself satisfying that p(a) = a. (i) Is the isomorphism from part (h) unique or can you find another isomorphism that is distinct from but also satisfies that (a) a? Justify your answer.

Consider the graph below with vertex set {a,b,c,d,e,f,g}. a Give the adjacency matrix of the graph with lexiographically ordered rows and columns.

a. Draw the directed graph corresponding to the adjacency matrix. [101] 1 0 2 2 Lo b. Using the adjacency matrix in (a) only, determine the number of walks of length 3 from each vertex to each other vertex.

Consider the map of New Islamabad Airport with wings: A-C and arms: a-o Wing -A Wing-C Wing-B Construct a graph for it, Build the Adjacency matrix for graph Eind Euler path