Graph Theory Questions Medium
The incidence matrix of a graph is a matrix that represents the relationship between the vertices and edges of a graph. It is a rectangular matrix with rows representing the vertices and columns representing the edges. Each entry in the matrix indicates whether a vertex is incident to an edge or not.
Specifically, the incidence matrix is defined as follows:
- If vertex v is incident to edge e, then the entry in the matrix corresponding to v and e is 1.
- If vertex v is not incident to edge e, then the entry in the matrix corresponding to v and e is 0.
In other words, the incidence matrix provides a binary representation of the adjacency between vertices and edges in a graph. It is a useful tool for analyzing and studying various properties of graphs, such as connectivity, planarity, and graph coloring.