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.
Question
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.
Solution
True. The incidence matrix of a graph is a matrix that represents the edges and vertices of a graph. Each row of the matrix represents an edge, and each column represents a vertex. If an edge is connected to a vertex, the corresponding cell in the matrix is 1, otherwise it is 0.
Since each edge in a graph connects two vertices, each row in the incidence matrix will have exactly two entries of 1. Therefore, the sum of all entries in the incidence matrix is twice the number of edges in the graph.
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