Orbit matrices of strongly regular graphs

Maksimović, Marija (2015) Orbit matrices of strongly regular graphs. Doctoral thesis, Faculty of Science > Department of Mathematics.

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Abstract

The subject of the thesis is a construction of orbit matrices of strongly regular graphs under the action of an assumed automorphism group and construction of strongly regular graphs and self-orthogonal codes obtained from orbit matrices. In the dissertation we have generalized an algorithm for constructing orbit matrices of strongly regular graphs under the action of the automorphism group of prime order, which was announced by M. Behbahani and C. Lam in 2011. The generalization resulted with an algorithm for the construction of orbit matrices of strongly regular graphs under the action of an automorphism group whose order may be a composite number. Computer programs were developed based on that generalized algorithm. We will also developed an algorithm and corresponding computer programs for the construction of adjacency matrices of strongly regular graphs obtained from the orbit matrix. By applying the developed algorithms and computer programs we constructed so far unknown strongly regular graphs with parameters (49,18,7,6). We made classification of strongly regular graphs with parameters (49,18,7,6) and strongly regular graphs with parameters (99,14,1,2) admitting an action of an automorphism of order 6. Furthermore, we studied the conditions under which orbit matrices of strongly regular graphs generate self-orthogonal linear co de. By applying this result we constructed self-orthogonal co des from orbit matrices of strongly regular graphs with various parameters and examined their properties.

Item Type: Thesis (Doctoral thesis)
Supervisor: Crnković, Dean
Date: 2015
Number of Pages: 132
Subjects: NATURAL SCIENCES > Mathematics > Algebra
NATURAL SCIENCES > Mathematics > Discrete end Combinatorial Mathematics
NATURAL SCIENCES > Mathematics > Mathematical Logic and Accounting
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 27 Apr 2015 12:31
Last Modified: 08 May 2015 09:59
URI: http://digre.pmf.unizg.hr/id/eprint/3888

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