### Abstract

In the present article, for bipartite graphs and chordal graphs, their exterior algebraic shifted graph and their symmetric algebraic shifted graph are studied. First, we will determine the symmetric algebraic shifted graph of complete bipartite graphs. It turns out that for a ≥ 3 and b ≥ 3, the exterior algebraic shifted graph of the complete bipartite graph Ka,b of size a, b is different from the symmetric algebraic shifted graph of Ka,b. Second, we will show that the exterior algebraic shifted graph of any chordal graph G coincides with the symmetric algebraic shifted graph of G. In addition, it will be shown that the exterior algebraic shifted graph of any chordal graph G is equal to some combinatorial shifted graph of G.

Original language | English |
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Pages (from-to) | 3071-3094 |

Number of pages | 24 |

Journal | Communications in Algebra |

Volume | 35 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2007 Oct 1 |

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### Keywords

- Algebraic shifting
- Bipartite graphs
- Chordal graphs
- Generic initial ideals

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Communications in Algebra*,

*35*(10), 3071-3094. https://doi.org/10.1080/00927870701405082