05733817

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05733817 Gu, Xiusong Sun, Zhiren Zhang, Jie The transformation graph $G^{xyz}$ when $xyz=--+$. J. Nanjing Norm. Univ., Nat. Sci. Ed. 32, No. 3, 12-14,18 (2009). 2009 Nanjing Normal University, Nanjing ZH transformation graph planar graph isomorphism Summary: The transformation graph $G^{- - +}$ of $G$ is the graph with vertex set $V (G)\cup E (G)$ in which the vertex $\alpha$ and $\beta$ are joined by an edge if one of the following conditions holds: { indent=7mm \item{(i)}$\alpha,\beta\in V (G)$, $\alpha$ and $\beta$ are not adjacent in $G$, \item{(ii)}$\alpha, \beta\in E (G)$, $\alpha$ and $\beta$ are not adjacent in $G$, \item{(iii)}$\alpha\in V (G),\beta\in E (G)$, and they are incident in $G$. } In this paper, it is shown that $G^{- - +}$ is not planar except for 12 graphs. It is also shown that for a graph $G,\ G^{- - +}\cong P_n^{- - +}$ if and only if $G\cong P_n$.