Question

The complete bipartite digraph $G_{m, n}$ is based on two disjoint sets of, respectively, $m$ and $n$ vertices. Each vertex in the first set is connected to each vertex in the second set by a single edge. (a) Draw $G_{2,3}, G_{2,4}$, and $G_{3,3}$. (b) Write the incidence matrix of each digraph. (c) How many edges does $G_{m, n}$ have? (d) How many independent circuits?

    The complete bipartite digraph $G_{m, n}$ is based on two disjoint sets of, respectively, $m$ and $n$ vertices. Each vertex in the first set is connected to each vertex in the second set by a single edge. (a) Draw $G_{2,3}, G_{2,4}$, and $G_{3,3}$. (b) Write the incidence matrix of each digraph. (c) How many edges does $G_{m, n}$ have? (d) How many independent circuits?

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Applied Linear Algebra (Undergraduate Texts in Mathematics)

Applied Linear Algebra (Undergraduate Texts in Mathematics)

Peter J. Olver,… 2nd Edition

Chapter 2, Problem 11

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Step 1

- For $G_{2,3}$, label two vertices on the left as $a_1$ and $a_2$, and three vertices on the right as $b_1$, $b_2$, and $b_3$. Draw directed edges from each vertex in the left set to each vertex in the right set. - For $G_{2,4}$, label two vertices on the left as Show more…

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The complete bipartite digraph $G_{m, n}$ is based on two disjoint sets of, respectively, $m$ and $n$ vertices. Each vertex in the first set is connected to each vertex in the second set by a single edge. (a) Draw $G_{2,3}, G_{2,4}$, and $G_{3,3}$. (b) Write the incidence matrix of each digraph. (c) How many edges does $G_{m, n}$ have? (d) How many independent circuits?

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