### Abstract

Motivated by a 1994 result of Graham et al. (Amer. Math. Monthly 101(7) (1994) 664) about spanning trees of the graphs with an antipodal isomorphism, we introduce the concept of k-pairable graphs and extend the result in Graham et al. (Amer. Math. Monthly 101(7) (1994) 664) to this larger class of graphs. We then define a new graph parameter p(G), called the pair length of graph G. This parameter measures the maximum distance, in some sense, between a subgraph induced by half the vertices of G with the isomorphic subgraph induced by the other half of V(G). An upper bound for the parameter p(G) is given. Some properties of the k-pairable graphs and their product graphs are studied. We also post some problems for further research.

Original language | English (US) |
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Pages (from-to) | 11-15 |

Number of pages | 5 |

Journal | Discrete Mathematics |

Volume | 287 |

Issue number | 1-3 |

DOIs | |

State | Published - Oct 28 2004 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*287*(1-3), 11-15. https://doi.org/10.1016/j.disc.2004.04.012

}

*Discrete Mathematics*, vol. 287, no. 1-3, pp. 11-15. https://doi.org/10.1016/j.disc.2004.04.012

**On k-pairable graphs.** / Chen, Zhibo.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On k-pairable graphs

AU - Chen, Zhibo

PY - 2004/10/28

Y1 - 2004/10/28

N2 - Motivated by a 1994 result of Graham et al. (Amer. Math. Monthly 101(7) (1994) 664) about spanning trees of the graphs with an antipodal isomorphism, we introduce the concept of k-pairable graphs and extend the result in Graham et al. (Amer. Math. Monthly 101(7) (1994) 664) to this larger class of graphs. We then define a new graph parameter p(G), called the pair length of graph G. This parameter measures the maximum distance, in some sense, between a subgraph induced by half the vertices of G with the isomorphic subgraph induced by the other half of V(G). An upper bound for the parameter p(G) is given. Some properties of the k-pairable graphs and their product graphs are studied. We also post some problems for further research.

AB - Motivated by a 1994 result of Graham et al. (Amer. Math. Monthly 101(7) (1994) 664) about spanning trees of the graphs with an antipodal isomorphism, we introduce the concept of k-pairable graphs and extend the result in Graham et al. (Amer. Math. Monthly 101(7) (1994) 664) to this larger class of graphs. We then define a new graph parameter p(G), called the pair length of graph G. This parameter measures the maximum distance, in some sense, between a subgraph induced by half the vertices of G with the isomorphic subgraph induced by the other half of V(G). An upper bound for the parameter p(G) is given. Some properties of the k-pairable graphs and their product graphs are studied. We also post some problems for further research.

UR - http://www.scopus.com/inward/record.url?scp=4644239388&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4644239388&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2004.04.012

DO - 10.1016/j.disc.2004.04.012

M3 - Article

VL - 287

SP - 11

EP - 15

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -