### 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 |
---|---|

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 |

Externally published | Yes |

### Fingerprint

### 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

**Algebraic shifting of finite graphs.** / Murai, Satoshi.

Research output: Contribution to journal › Article

*Communications in Algebra*, vol. 35, no. 10, pp. 3071-3094. https://doi.org/10.1080/00927870701405082

}

TY - JOUR

T1 - Algebraic shifting of finite graphs

AU - Murai, Satoshi

PY - 2007/10/1

Y1 - 2007/10/1

N2 - 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.

AB - 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.

KW - Algebraic shifting

KW - Bipartite graphs

KW - Chordal graphs

KW - Generic initial ideals

UR - http://www.scopus.com/inward/record.url?scp=34848891523&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34848891523&partnerID=8YFLogxK

U2 - 10.1080/00927870701405082

DO - 10.1080/00927870701405082

M3 - Article

AN - SCOPUS:34848891523

VL - 35

SP - 3071

EP - 3094

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 10

ER -