Graphical Indices and their Applications

The biochemical community has been using graphical (topological, chemical) indices in the study of Quantitative Structure-Activity Relationships (QSAR) and Quantitative Structure-Property Relationships (QSPR), as they have been shown to have strong correlations with the chemical properties of certain chemical compounds (i.e. boiling point, surface area, etc.). We examine some of these chemical indices and closely related pure graph theoretical indices: the Randić index, the Wiener index, the degree distance, and the number of subtrees. We find which structure will maximize the Randić index of a class of graphs known as cacti, and we find a functional relationship between the Wiener index and the degree distance for several types of graphs. We also develop an algorithm to find the structure that maximizes the number of subtrees of trees, a characterization of the second maximal tree may also follow as an immediate result of this algorithm.

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2010

Author dc:creator

• Gray, Daniel

Contributors dc:contributor

• Goran Lesaja
• Yan Wu

• ETD
• Trees
• Subtrees
• Cacti
• Randić index
• Wiener index
• Degree distance
• Graphical indices
• QSAR (Biochemistry)
• Biochemistry
• Graph algorithms
• Graph theory

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/659

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-1659