If the incidence matrix of a graph has five identical columns, then the graph G has
Question
If the incidence matrix of a graph has five identical columns, then the graph G has
Solution
The graph G has five identical vertices.
Here's why:
In graph theory, an incidence matrix is a matrix that shows the relationship between two classes of objects. If one class is the vertex set and the other is the edge set, then the incidence matrix is called a vertex-edge incidence matrix.
The columns of the incidence matrix represent the vertices of the graph, and the rows represent the edges. If a graph has five identical columns in its incidence matrix, this means that there are five vertices in the graph that have the exact same connections to the edges of the graph. In other words, these five vertices are identical in terms of their relationships with other vertices in the graph.
Similar Questions
For an undirected graph with 𝑛n vertices and 𝑚m edges, the incidence matrix has:A. 𝑛n rows and 𝑚m columnsB. 𝑚m rows and 𝑛n columnsC. 𝑛n rows and 𝑛n columnsD. 𝑚m rows and 𝑚m columns
True or False: The sum of the entries in the incidence matrix of any graph is equal to twice the number of edges in the graph.
If a connected Graph (G) contains n vertices what would be the rank of its incidence matrix?Group of answer choicesn-1values greater than n are possiblevalues less than n-1 are possibleinsufficient Information is given
The column sum in an incidence matrix for a directed graph having no self loop is __________?Group of answer choices012equal to the number of edges
True or False: The adjacency matrix for any graph with 5 edges has 5 rows and 5 columns.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.