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On the Determination Problem for P 4-Transformation of Graphs

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Abstract

We prove that the P 4-transformation is one-to-one on the set of graphs with minimum degree at least 3, and if graphs G and G ' have minimum degree at least 3 then any isomorphism from the P 4-graph P 4(G) to the P 4-graph P 4(G ') is induced by a vertex-isomorphism from G to G ' unless G and G ' both belong to a special family of graphs.

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Authors and Affiliations

  1. Center for Combinatorics and LPMC-TJKLC, Nankai University, Tianjin, 300071, China

    Xueliang Li & Yan Liu

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  1. Xueliang Li
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  2. Yan Liu
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Correspondence to Xueliang Li.

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Supported by NSFC, PCSIRT and the “973” program.

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Li, X., Liu, Y. On the Determination Problem for P 4-Transformation of Graphs. Graphs and Combinatorics 24, 551–562 (2008). https://doi.org/10.1007/s00373-008-0808-6

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