### Abstract

The concept of the k-pairable graphs was introduced by Zhibo Chen (On k-pairable graphs, Discrete Mathematics 287 (2004), 11-15) as an extension of hypercubes and graphs with an antipodal isomorphism. In the same paper, Chen also introduced a new graph parameter p(G), called the pair length of a graph G, as the maximum k such that G is k-pairable and p(G) = 0 if G is not k-pairable for any positive integer k. In this paper, we answer the two open questions raised by Chen in the case that the graphs involved are restricted to be trees. That is, we characterize the trees G with p(G) = 1 and prove that p(G □ H) = p(G) + p(H) when both G and H are trees.

Original language | English (US) |
---|---|

Pages (from-to) | 377-386 |

Number of pages | 10 |

Journal | Czechoslovak Mathematical Journal |

Volume | 57 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Czechoslovak Mathematical Journal*,

*57*(1), 377-386. https://doi.org/10.1007/s10587-007-0066-4

}

*Czechoslovak Mathematical Journal*, vol. 57, no. 1, pp. 377-386. https://doi.org/10.1007/s10587-007-0066-4

**On k-pairable graphs from trees.** / Che, Zhongyuan.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On k-pairable graphs from trees

AU - Che, Zhongyuan

PY - 2007/3/1

Y1 - 2007/3/1

N2 - The concept of the k-pairable graphs was introduced by Zhibo Chen (On k-pairable graphs, Discrete Mathematics 287 (2004), 11-15) as an extension of hypercubes and graphs with an antipodal isomorphism. In the same paper, Chen also introduced a new graph parameter p(G), called the pair length of a graph G, as the maximum k such that G is k-pairable and p(G) = 0 if G is not k-pairable for any positive integer k. In this paper, we answer the two open questions raised by Chen in the case that the graphs involved are restricted to be trees. That is, we characterize the trees G with p(G) = 1 and prove that p(G □ H) = p(G) + p(H) when both G and H are trees.

AB - The concept of the k-pairable graphs was introduced by Zhibo Chen (On k-pairable graphs, Discrete Mathematics 287 (2004), 11-15) as an extension of hypercubes and graphs with an antipodal isomorphism. In the same paper, Chen also introduced a new graph parameter p(G), called the pair length of a graph G, as the maximum k such that G is k-pairable and p(G) = 0 if G is not k-pairable for any positive integer k. In this paper, we answer the two open questions raised by Chen in the case that the graphs involved are restricted to be trees. That is, we characterize the trees G with p(G) = 1 and prove that p(G □ H) = p(G) + p(H) when both G and H are trees.

UR - http://www.scopus.com/inward/record.url?scp=33947414470&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33947414470&partnerID=8YFLogxK

U2 - 10.1007/s10587-007-0066-4

DO - 10.1007/s10587-007-0066-4

M3 - Article

AN - SCOPUS:33947414470

VL - 57

SP - 377

EP - 386

JO - Czechoslovak Mathematical Journal

JF - Czechoslovak Mathematical Journal

SN - 0011-4642

IS - 1

ER -