On the Determination Problem for P4-Transformation of
Graphs
Yan Liu
Center for Combinatorics and LPMC, Nankai University, Tianjin 300071, P. R.
China
Abstract Full Text PDF
For graphs $G$ and $G^{'}$ with
minimum degree $\delta=3$, we prove that the $P_4$-transformation
is one-to-one, and any isomorphism from the $P_4$-graph $P_4(G)$
to $P_4(G^{'})$ can be induced by a vertex-isomorphism of $G$ onto
$G^{'}$ except for a special family of graphs.