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# Zero Forcing Sets for Distance Regular Graphs

Oosterman, R.A. (2014) Zero Forcing Sets for Distance Regular Graphs. Bachelor's Thesis, Mathematics.

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## Abstract

In this project, linear systems on graphs are studied, representing a multi-agent system with leader and follower agents. These agents operate individually, but are able to interchange information with each other. Leader agents obtain input, follower agents do not. Depending on a certain set of leader agents, also named as a leader set, the system defined on its graph may be controllable. Therefore, the main purpose of this research is finding a feasible leader set for a certain graph such that the corresponding system is controllable. To reach this, one has to assign vertices as leader agents in a specific way. These vertices are assigned according to the so-called zero forcing principle. Leaders sets for which a certain system is controllable are said to be a zero forcing sets. When a solution is found, the zero forcing process can only determine whether a system is controllable for a given leader set. Unfortunately, it is not yet possible to assign these vertices in a straightforward manner, and it turns out that it is not even possible to verify whether this leader set is minimal. In order to still be able find feasible leader sets, a number of algorithms is descibed in this project. The class of distance regular graphs is treated most extensively, as this is the class of graphs which the given algorithms apply to. For certain graphs for which they are known to be distance regular, the algoritms are tested, and the result with the fewest possible leaders is taken. Comparing to certain properties of these graphs, such as the maximal eigenvalue multiplicity, one can finally decide whether the found leader set is optimal or not.

Item Type: Thesis (Bachelor's Thesis) Mathematics Bachelor's Thesis English 15 Feb 2018 07:57 15 Feb 2018 07:57 https://fse.studenttheses.ub.rug.nl/id/eprint/11834

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