Bipartite half

In graph theory, the bipartite half or half-square of a bipartite graph $G = (U, V, E)$ is a graph whose vertex set is one of the two sides of the bipartition (without loss of generality, $U$ ) and in which there is an edge $u i u j$ for each pair of vertices $u i, u j$ in $U$ that are at distance two from each other in $G$ .^[1] That is, in a more compact notation, the bipartite half is $G 2 [U]$ where the superscript 2 denotes the square of a graph and the square brackets denote an induced subgraph.

^ Wilson, Robin J. (2004), Topics in Algebraic Graph Theory, Encyclopedia of Mathematics and its Applications, vol. 102, Cambridge University Press, p. 188, ISBN 9780521801973.

[1] Wilson, Robin J. (2004), Topics in Algebraic Graph Theory, Encyclopedia of Mathematics and its Applications, vol. 102, Cambridge University Press, p. 188, ISBN 9780521801973.

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