IB Mathematics Applications & Interpretation Topic…

A directed graph models a data network with nodes $P, Q, R, S$ , and $T$ , representing servers, and directed edges indicating one-way data transmission. A directed graph with nodes $P,Q,R,S,T$ and directed edges , , , , , .

(a) Write down the adjacency matrix $M$ for this graph, with rows and columns ordered $P, Q, R, S, T$ .

(b) Find the number of distinct walks of length 5 from $P$ to $R$ .

(e) a lower bound for the van's total distance by deleting vertex $A$ , finding an MST on the remaining vertices, and adding the two shortest edges incident to $A$ .

(e) a lower bound for the van's tour distance using the MST from part (b).

(e) In the updated network, the number of walks of length 4 from $U$ to $P$ .

(e) Using the updated matrix, find the number of triangles (cycles of length 3) including vertex $U$ .

(a) Write down the adjacency matrix $M$ for this graph, with rows and columns ordered $P, Q, R, S, T$ .

(b) Find the number of distinct walks of length 5 from $P$ to $R$ .

(d) A new server $U$ is added. Add directed edges $Q\to U$ and $U\to R$ . Update the adjacency matrix and redraw the graph, with rows and columns ordered $P, Q, R, S, T, U$ .

(a) Write down the adjacency matrix $M$ for this graph, with rows and columns ordered $A, B, C, D, E$ .

(b) Use Kruskal's algorithm to find the minimum spanning tree (MST), listing the edges in the order they are selected.

(d) A delivery van must visit all warehouses, starting and ending at $A$ . Use the nearest neighbor algorithm to find an upper bound for the total distance.

(d) A delivery van must visit each warehouse exactly once, starting and ending at $A$ . Use the nearest neighbor algorithm to find an upper bound for the total distance.

(d) A new server $U$ is added, receiving data from $Q$ and sending to $R$ . Update the adjacency matrix and redraw the graph.

A social network is modeled as a graph with vertices $V, W, X, Y, Z$ , representing users, and edges indicating direct friendships. The adjacency matrix $M$ is:

M=\left(\begin{array}{lllll} 0 & 1 & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 1 & 0 \end{array}\right)

(a) the degree of each vertex.

(b) Find the number of walks of length 5 from $V$ to $Y$ .

(d) The network adds a new user $U$ , connected to $W$ and $Y$ . Update the adjacency matrix and redraw the graph.

(a) Write down the adjacency matrix $M$ for this graph, with rows and columns ordered $A, B, C, D, E$ .

(b) Use Kruskal's algorithm to find the minimum spanning tree (MST), listing the edges in the order they are selected.

(e) In the updated network, the number of walks of length 4 from $U$ to $P$ .

A logistics company operates a network of warehouses labeled $A, B, C, D$ , and $E$ , connected by direct delivery routes with weights representing distances (in km). The weighted graph is shown below.

A directed graph models a data network with nodes $P, Q, R, S$ , and $T$ , representing servers, and directed edges indicating one-way data transmission.

IB Mathematics Applications & Interpretation AHL 3.15—adjacency Matrices and Tables Questionbank

IB Mathematics Applications & Interpretation AHL 3.15—adjacency Matrices and Tables Questionbank

IB Mathematics Applications & Interpretation AHL 3.15—adjacency Matrices and Tables Questionbank

IB Mathematics Applications & Interpretation AHL 3.15—adjacency Matrices and Tables Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 3.15—adjacency Matrices and Tables Questionbank