29.1.4. Question 3

Try these first

1. 1.

   What does the incidence matrix represent in a graph?

   Hint

   Think about how we depict connections in a graph.

2. 2.

   What do you obtain when you multiply an incidence matrix by its transpose?

   Hint

   Consider how vertex connections change through multiplication.

3. 3.

   What is the primary function of an incidence matrix in graph theory?

   • To represent vertices only
   • To show connections between vertices and edges
   • To compute the degree of a vertex

   Hint

   Remember what an incidence matrix specifically tracks.

4. 4.

   The diagonal entries of the product of B and B^T represent what?

   • Sinuses
   • The lengths of edges
   • The degree of each vertex

   Hint

   Consider what a vertex's degree signifies in graph theory.

5. 5.

   Create a complete graph K4 and derive its incidence matrix and the product with its transpose.

   Hint

   Remember that K4 will have edges connecting every vertex to every other vertex.

6. 6.

   Given a graph structure with 5 vertices and 4 edges, provide potential incidence matrices and calculate their products.

   Hint

   Draw the graph and note its edges before constructing the incidence matrix.