#### Presentation Title

Leech-Type Questions of Trees

#### Location

Room 1909

#### Session Format

Paper Presentation

#### Research Area Topic:

Natural & Physical Sciences - Mathematics

#### Co-Presenters, Co- Authors, Co-Researchers, Mentors, or Faculty Advisors

Faculty Advisor: Dr. Hua Wang

Co-Authors: Dr. Hua Wang and Mr. Mustafa Ozen.

#### Abstract

*In 1975, John Leech brought forward a problem about finding positive integer-weighted trees with n vertices such that weighted distances between pairs of vertices are exactly the consecutive positive integers starting from 1. **This question is motivated from Electrical Engineering in order to find an efficient design for resistances in electrical circuits and later became interesting to computer scientists and mathematicians in addition to engineers. **Only five Leech trees are known and over the years, some non-existence results have been demonstrated. **In this talk, we are going to give an introduction to Leech Tree. **Since there are no more Leech tree on n vertices, we will try to find next best weighted tree and generalize the concept. In other words**, we will examine variations of such "Leech type" tree labeling questions **including the Modular Leech Tree, 'almost' Leech tree and in particular, the Leaf-Leech tree. Observations and relationships regarding their structures will be presented, analogous to those established for the original Leech trees.*

#### Keywords

Leech tree, Modular Leech tree, Distances between leaves

#### Presentation Type and Release Option

Presentation (Open Access)

#### Start Date

4-24-2015 1:30 PM

#### End Date

4-24-2015 2:30 PM

#### Recommended Citation

Yalman, Demet, "Leech-Type Questions of Trees" (2015). *Georgia Southern University Research Symposium*. 72.

https://digitalcommons.georgiasouthern.edu/research_symposium/2015/2015/72

Leech-Type Questions of Trees

Room 1909

*In 1975, John Leech brought forward a problem about finding positive integer-weighted trees with n vertices such that weighted distances between pairs of vertices are exactly the consecutive positive integers starting from 1. **This question is motivated from Electrical Engineering in order to find an efficient design for resistances in electrical circuits and later became interesting to computer scientists and mathematicians in addition to engineers. **Only five Leech trees are known and over the years, some non-existence results have been demonstrated. **In this talk, we are going to give an introduction to Leech Tree. **Since there are no more Leech tree on n vertices, we will try to find next best weighted tree and generalize the concept. In other words**, we will examine variations of such "Leech type" tree labeling questions **including the Modular Leech Tree, 'almost' Leech tree and in particular, the Leaf-Leech tree. Observations and relationships regarding their structures will be presented, analogous to those established for the original Leech trees.*