Final answer:
The sum of entries in a row of the incidence matrix for an undirected graph equals the degree of the vertex corresponding to that row as each '1' in the row indicates an edge connected to that vertex.
Step-by-step explanation:
The sum of the entries in a row of the incidence matrix for an undirected graph is equal to the degree of the vertex corresponding to that row. An incidence matrix is a matrix that shows the relationship between vertices and edges in a graph. In this matrix, each row represents a vertex and each column represents an edge.
For an undirected graph, an entry in the incidence matrix will be '1' if the vertex at that row is incident to the edge at that column and '0' otherwise.
So, if we consider a vertex 'v', the sum of the entries in the row corresponding to vertex 'v' represents the total number of edges incident to 'v'.
Since each edge contributes to one degree at the vertex it is incident upon, the sum is equivalent to the degree of 'v', which is the total number of edges connected to that vertex.
In an undirected graph, the incidence matrix is a matrix that represents the connections between vertices and edges. Each row of the incidence matrix corresponds to a vertex, and each column corresponds to an edge.
The entries in the row for a particular vertex are 1 if that vertex is incident to the corresponding edge, and 0 otherwise.