## Abstract

Given a tree T and a vertex v in T, the number of subtrees of T containing v is denoted by η_{T}(v) and called the subtree number at v. Similarly, η_{T}(u,v) denotes the number of subtrees of T that contain both u and v. Motivated from the distance function and the eccentricity at a vertex, we study the eccentric subtree number at a vertex v in T, defined as η_{T}^{ecc}(v)=minu∈V(T)η_{T}(v,u). This concept provides us a new perspective in the study of the well-known correlation between the distance and the subtree numbers. We will present properties of the eccentric subtree number analogous to those related to the eccentricity and center of a tree, as well as some extremal results with respect to the eccentric subtree number and sum of eccentric subtree numbers in a tree. Some open problems for further study are also proposed.

Original language | English |
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Pages (from-to) | 123-132 |

Number of pages | 10 |

Journal | Discrete Applied Mathematics |

Volume | 290 |

DOIs | |

State | Published - Feb 15 2021 |

## Keywords

- Eccentricity
- Subtree
- The eccentric subtree number