#### Presentation Title

Greedy Trees and Degree Sequences

#### Location

Room 2905 A

#### Session Format

Paper Presentation

#### Research Area Topic:

Natural & Physical Sciences - Mathematics

#### Abstract

Graph invariants known as topological indices are frequently used in applied mathematics, biochemistry and other related fields to describe the structure of an object that has often close correlation with various properties such as boiling point of a chemical. Among them, a group of indices defined on the degrees of adjacent vertices have been studied extensively. During this talk we will provide a general characterization for the extremal structures with respect to such indices defined on a particular type of functions.

We consider a function on adjacent degrees of a tree, T, to be f(x,y) and the connectivity function associated with f. We first introduce the extremal tree structures, with a given degree sequence, that maximize or minimize such functions. When a partial ordering, called "majorization'', is defined on the degree sequences of trees on n vertices, we compare the extremal trees of different degree sequences. This results in many extemal results as immediate consequences. We will also briefly discuss these applications.

#### Presentation Type and Release Option

Presentation (Open Access)

#### Start Date

4-16-2016 1:30 PM

#### End Date

4-16-2016 2:30 PM

#### Recommended Citation

Bass, Rachel, "Greedy Trees and Degree Sequences" (2016). *Georgia Southern University Research Symposium*. 170.

https://digitalcommons.georgiasouthern.edu/research_symposium/2016/2016/170

Greedy Trees and Degree Sequences

Room 2905 A

Graph invariants known as topological indices are frequently used in applied mathematics, biochemistry and other related fields to describe the structure of an object that has often close correlation with various properties such as boiling point of a chemical. Among them, a group of indices defined on the degrees of adjacent vertices have been studied extensively. During this talk we will provide a general characterization for the extremal structures with respect to such indices defined on a particular type of functions.

We consider a function on adjacent degrees of a tree, T, to be f(x,y) and the connectivity function associated with f. We first introduce the extremal tree structures, with a given degree sequence, that maximize or minimize such functions. When a partial ordering, called "majorization'', is defined on the degree sequences of trees on n vertices, we compare the extremal trees of different degree sequences. This results in many extemal results as immediate consequences. We will also briefly discuss these applications.