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Projects / Programmes source: ARIS

Graph Products and Metric Graph Theory

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Periods
January 1, 1999 - December 31, 2003
Research activity

Code Science Field Subfield
1.01.00  Natural sciences and mathematics  Mathematics   

Code Science Field
P110  Natural sciences and mathematics  Mathematical logic, set theory, combinatories 
P170  Natural sciences and mathematics  Computer science, numerical analysis, systems, control 
P410  Natural sciences and mathematics  Theoretical chemistry, quantum chemistry 
Evaluation (rules)
source: COBISS
Evaluation of bibliographic research performance indicators according to ARIS methodology
Citations Citations for bibliographic records in COBIB.SI that are linked to records in citation databases
source: WoS source: Scopus source: COBISS
Researchers (4)
no. Code Name and surname Research area Role Period No. of publications
1.  05949  PhD Sandi Klavžar  Mathematics  Head  2001 - 2003  1,177 
2.  08727  PhD Uroš Milutinović  Mathematics  Researcher  2001 - 2003  348 
3.  11666  PhD Aleksander Vesel  Computer intensive methods and applications  Researcher  2001 - 2003  339 
4.  15571  PhD Blaž Zmazek  Mathematics  Researcher  2001 - 2003  253 
Organisations (1)
no. Code Research organisation City Registration number No. of publications
1.  0101  Institute of Mathematics, Physics and Mechanics  Ljubljana  5055598000  20,221 
Abstract
Graph products, their invariants and related topics will be considered. Median graphs will also be studied with emphasis on recognition problem. New characterizations and properties of median graphs will be developed for this purpose. We will also try to generalize some of these results to the non-bipartite case, in particular to partial Hamming graphs and quasi-median graphs. Besides median graphs other classes of isometric subgraphs of hypercubes will be also considered: partial cubes, semi-median graphs, almost-median graphs, acyclic cubical complexes, quasi-median graphs and partial Hamming graphs. A special emphasis will be given to the study of hierarchy of these classes of graphs and their connections with the so-called expansion procedures. Metric graph theory will be applied in chemical graph theory for computing several topological invariants, for instance the Wiener index and the Hyper-Wiener index. We will also consider clique-gated graphs and the problem of computing the smallest number of linear forests. In the area of algorithmic graph theory we plan to consider and develop fast recognition algorithms for the above mentioned classes of graphs, in particular for median graphs, acyclic cubical complexes and semi-median graphs. We will also try to obtain some nontrivial lower bound for the recognition complexities of these classes. In addition, we will also study problems connected to the generalizations of the classical Tower of Hanoi problem. One of the main goals of the research group is a monograph that will cover graph products, their isometric subgraphs, and related topics.
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