Path graphs
Hajo J. Broersma, Cornells Hoede · Journal of Graph Theory · 1989
Abstract The concept of a line graph is generalized to that of a path graph. The path graph Pk(G) of a graph G is obtained by representing the paths Pk in G by vertices and joining two vertices whenever the corresponding paths Pk in G form a path Pk+1 or a cycle Ck. P3‐graphs are characterized and investigated on isomorphism and traversability. Trees and unicyclic graphs with hamiltonian P3‐graphs are characterized.