# Constructing all Possible Leaves for Maximum Packings of the Complete Graph with Stars of Sizes Six and Seven

## Major

Mathematics

## Submission Type

Poster

## Area of Study or Work

Mathematics

## Expected Graduation Date

2023

## Location

CNS Atrium, Easel 18

## Start Date

4-15-2023 10:30 AM

## End Date

4-15-2023 11:45 AM

## Abstract

A 6-star is the complete bipartite graph **K _{1,6}**. A packing of

**K**with 6-stars is a set of edge disjoint subgraphs of

_{n}**K**, each of which is isomorphic to

_{n}**S**. The set of edges of

_{6}**K**which are not used in the packing is called the leave and is denoted by

_{n}**. The packing is called maximum if**

*L***|**| is minimum with respect to all such packings. We show that every possible leave graph is achievable as the leave of a maximum packing of

*L***K**with 6-stars and 7-stars.

_{n}Constructing all Possible Leaves for Maximum Packings of the Complete Graph with Stars of Sizes Six and Seven

CNS Atrium, Easel 18

A 6-star is the complete bipartite graph **K _{1,6}**. A packing of

**K**with 6-stars is a set of edge disjoint subgraphs of

_{n}**K**, each of which is isomorphic to

_{n}**S**. The set of edges of

_{6}**K**which are not used in the packing is called the leave and is denoted by

_{n}**. The packing is called maximum if**

*L***|**| is minimum with respect to all such packings. We show that every possible leave graph is achievable as the leave of a maximum packing of

*L***K**with 6-stars and 7-stars.

_{n}