1 research outputs found
On some subclasses of circular-arc catch digraphs
Catch digraphs was introduced by Hiroshi Maehera in 1984 as an analog of
intersection graphs where a family of pointed sets represents a digraph. After
that Prisner continued his research particularly on interval catch digraphs by
characterizing them diasteroidal triple free. It has numerous applications in
the field of real world problems like network technology and telecommunication
operations. In this article we introduce a new class of catch digraphs, namely
circular-arc catch digraphs. The definition is same as interval catch digraph,
only the intervals are replaced by circular-arcs here. We present the
characterization of proper circular-arc catch digraphs, which is a natural
subclass of circular-arc catch digraphs where no circular-arc is contained in
other properly. We do the characterization by introducing a concept monotone
circular ordering for the vertices of the augmented adjacency matrices of it.
Next we find that underlying graph of a proper oriented circular-arc catch
digraph is a proper circular-arc graph. Also we characterize proper oriented
circular-arc catch digraphs by defining a certain kind of circular vertex
ordering of its vertices. Another interesting result is to characterize
oriented circular-arc catch digraphs which are tournaments in terms of
forbidden subdigraphs. Further we study some properties of an oriented
circular-arc catch digraph. In conclusion we discuss the relations between
these subclasses of circular-arc catch digraphs