On the Determination Problem for P4-Transformation of Graphs

Yan Liu
Center for Combinatorics and LPMC, Nankai University, Tianjin 300071, P. R. China


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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.