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

This document is currently not available here.

Share

COinS
 
Apr 24th, 1:30 PM Apr 24th, 2:30 PM

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.