Exercise · ZW-BIPARTITE-GRAPH-007 · ★★☆ Intermediate

In a bipartite graph, the 4 vertices of part \(A\) all have degree 3 and the 6 vertices of \(B\) all have the same degree \(d\). What is \(d\)?

Choose one option.

Show answer
  • A. 2

Explanation

Each edge has one endpoint in each part, so both degree sums equal \(|E|\): \(4\cdot3=12=6d\) and \(d=2\).

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Review the concept: Bipartite graph

A bipartite graph is a graph \(G=(V,E)\) whose vertices split into two disjoint sets \(A\) and \(B\) so that every edge \(e\in E\) joins a vertex of \(A\) to one of \(B\).

\[V=A\cup B,\quad A\cap B=\varnothing,\quad |e\cap A|=1\ \text{ for every } e\in E\]

More practice problems: bipartite graph

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