Neki rezultati o ekstremnim vrednostima Randićevog indeksa na grafovima
Докторанд
Divnić, TomicaМентор
Pavlović, LjiljanaЧланови комисије
Kovačević-Vujčić, VeraPetrović, Miroslav
Метаподаци
Приказ свих података о дисертацијиСажетак
This doctoral dissertation belongs to the Combinatorial Optimization applied to
graphs, which includes elements of Linear and Quadratic Programming and Graph
Theory.
Combinatorial Optimization, as special mathematical discipline, is relatively young, although the first papers are more than two hundred years old. The fast
development emerges after the second wold war, when grows need for optimization
many tasks and processes. Since many objects could be represents as graph and
combinatorial optimization solve extremal problems on discrete structures, there is narrow connection with Graph Theory.
The subject of this dissertation is finding minimal value of the Randi´c index on
n-vertex graphs G(k, n) with given minimum degree k of vertices and describing the
structure of extremal graphs. This index was introduced 1975 by chemist Milan
Randi´c in order to measure the branching of some molecules. There is a good
correlations between this index and some physico-chemical properties of alcane...s.
There is, also, connection between Randi´c index and the eigenvalues of the Laplacian matrix of graph.