# relabelBipartite -- relabels a bipartite graph so all vertices of a given class are contiguous

## Synopsis

• Usage:
L' = relabelBipartite L
T = relabelBipartite S
H = relabelBipartite G
• Inputs:
• L, a list, a list of bipartite graphs in various formats
• S, , a bipartite graph encoded in either Sparse6 or Graph6 format
• G, , a bipartite graph
• Outputs:
• L', a list, a list of graphs isomorphic to $S$
• T, , a graph isomorphic to $S$ encoded in either Sparse6 or Graph6 format
• H, , a graph isomorphic to $G$

## Description

A bipartite graph can be labeled so all vertices of a given class are contiguous. This method does precisely that to a bipartite graph.

 i1 : R = QQ[a..f]; i2 : G = graph flatten apply({a,c,e}, v->v*{b,d,f}) o2 = Graph{edges => {{a, b}, {b, c}, {a, d}, {c, d}, {b, e}, {d, e}, {a, f}, {c, f}, {e, f}}} ring => R vertices => {a, b, c, d, e, f} o2 : Graph i3 : relabelBipartite G o3 = Graph{edges => {{a, d}, {b, d}, {c, d}, {a, e}, {b, e}, {c, e}, {a, f}, {b, f}, {c, f}}} ring => R vertices => {a, b, c, d, e, f} o3 : Graph

If any of the inputs are not bipartite graphs, then the method throws an error.