{"id":{"repo_id":"gsu","oai_identifier":"oai:digitalcommons.georgiasouthern.edu:etd-1659"},"canonical_url":"https://search.dev.ndltd.org/etd/gsu/oai:digitalcommons.georgiasouthern.edu:etd-1659","repository":{"repo_id":"gsu","name":"Georgia Southern University","base_url":"https://digitalcommons.georgiasouthern.edu/do/oai/"},"display":{"title":"Graphical Indices and their Applications","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Gray, Daniel"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (open access)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Goran Lesaja","Yan Wu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-05-01T07:00:00Z","date_published":"2010-05-01T07:00:00Z","updated_at":"2026-07-24T02:27:19Z","subjects":["ETD","Trees","Subtrees","Cacti","Randić index","Wiener index","Degree distance","Graphical indices","QSAR (Biochemistry)","Biochemistry","Graph algorithms","Graph theory"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/659","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Goran Lesaja","Yan Wu"]},{"key":"dc:creator","label":"Author","values":["Gray, Daniel"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-10-17T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (open access)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Trees","Subtrees","Cacti","Randić index","Wiener index","Degree distance","Graphical indices","QSAR (Biochemistry)","Biochemistry","Graph algorithms","Graph theory"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/659"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Graphical Indices and their Applications"]}]}],"canonical_facts":{"dc:contributor":["Goran Lesaja","Yan Wu"],"dc:creator":["Gray, Daniel"],"dc:date.available":["2013-10-17T07:00:00Z"],"dc:description.abstract":["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."],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/659"],"dc:subject":["ETD","Trees","Subtrees","Cacti","Randić index","Wiener index","Degree distance","Graphical indices","QSAR (Biochemistry)","Biochemistry","Graph algorithms","Graph theory"],"dc:title":["Graphical Indices and their Applications"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (open access)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:27:19Z"}