The adjacency matrix of a graph can be interpreted as the incidence matrix of a design, or as the generator matrix of a binary code. Here these relations play a central role. We consider graphs for which the corresponding design is a (symmetric) block design or (group) divisible design. Such graphs are strongly regular (in case of a block design) or very similar to a strongly regular graph (in case of a divisible design). Many constructions and properties for these kind of graphs are obtained. We also consider the binary code of a strongly regular graph, work out some theory and give several examples.
|Title of host publication||Information Security, Coding Theory and Related Combinatorics|
|Subtitle of host publication||Information coding and combinatories|
|Editors||D. Crnkovic, V. Tonchev|
|Place of Publication||Amsterdam|
|Number of pages||460|
|Publication status||Published - 2011|
|Name||NATO Science for Peace and Security Series - D: Information and Communication Security|
Haemers, W. H. (2011). Matrices for graphs designs and codes. In D. Crnkovic, & V. Tonchev (Eds.), Information Security, Coding Theory and Related Combinatorics: Information coding and combinatories (pp. 253-277). (NATO Science for Peace and Security Series - D: Information and Communication Security; No. 29). IOS Press.