On one hand the content of this thesis falls within the scope of Group theory, and on
the other hand in the field of Graph theory. The thesis deals with Cayley digraphs of
different finite groups and with identifying properties of groups from their representation
as Cayley (di)graphs. By the properties of groups we particularly refer to the properties
such as the orders of elements, generators of group, the subgroups, the normal subgroups,
the cosets, and so on. Cayley digraphs are very appropriate for such consideration as they
directly or indirectly reveal various properties of the groups, and give a clear insight into
the complexity of the group.
Cayley (di)graphs are named after Arthur Cayley, who first mentioned them in 1878.
These graphs are naturally obtained from groups with their vertices being the elements of
the group in question. Due to the symmetry these graphs \look\ exactly the same from
each vertex. When investigating the properties of the groups we examine the structure
of their Cayley (di)graphs and their characteristics. Groups are in fact abstract objects.
Being able to investigate their properties via their Cayley (di)graphs is thus of great help
since it enables us to visualise these abstract objects.
At the beginning of the thesis we define the basic concepts of Group theory that are needed
to understand the thesis. After that we explain the basic concepts of Graph theory
and introduce a concept of the digraph. Afterwards we introduce the concept of Cayley
(di)graphs, which play a central role in the thesis. In particular, we indicate how the properties
of the group are re
ected in their Cayley (di)graphs and how these characteristics
can be determined.
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