Discussion
V = {A, B, C, D, E, F, G, H, I}
E = {e1 = (A, B), e2 = (A, C), e3 = (A, D), e4 = (B, C), e5 = (B, F), e6 = (B, H), e7 = (C, D), e8 = (C, E), e9 = (C, F), e10 = (D, E), e11 = (D, I), e12 = (E, F), e13 = (E, G), e14 = (F, G), e15 = (F, H), e16 = (G, H), e17 = (G, I), e18 = (H, I)}
W = {22, 9, 12, 35, 36, 34, 4, 33, 30, 18, 23, 24, 39, 25, 21, 19}
The order of node (vertex)-edge incidence matrix for the undirected graph is .................. .
Answer: B
The incidence matrix is 9×18.
A node (vertex)-edge incidence matrix has one row for each vertex and one column for each edge; entry (i, j) is 1 when vertex i is an end of edge j. The graph has 9 vertices (A to I) and 18 edges (e1 to e18), so the matrix is 9 rows by 18 columns. Each column holds exactly two 1s, because every edge of an undirected graph has two ends.
18×9 is the transpose, an edge-vertex arrangement. 9×9 is the size of the adjacency matrix, and 18×18 matches nothing. The weight set W does not affect the order of the matrix.
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