P3-isomorphisms for graphs
Robert E. L. Aldred, Mark N. Ellingham, Robert L. Hemminger, Peter Jipsen · Journal of Graph Theory · 1997
The P3-graph of a finite simple graph G is the graph whose vertices are the 3-vertex paths of G, with adjacency between two such paths whenever their union is a 4-vertex path or a 3-cycle. In this paper we show that connected fnite simple graphs G and H with isomorphic P3-graphs are either isomorphic or part of three exceptional families. We also characterize all isomorphisms between P3-graphs in terms of the original graphs. © 1997 John Wiley & Sons, Inc. J Graph Theory 26:35–51, 1997