| dc.description.abstract | The complexity in building massive scale parallel
processing systems has re- sulted in a growing interest in the study
of interconnection networks design. Network design a®ects the
performance, cost, scalability, and availability of parallel
computers. Therefore, discovering a good structure of the network is
one of the basic issues. From modeling point of view, the structure
of networks can be naturally stud- ied in terms of graph theory.
Several common desirable features of networks, such as large number
of processing elements, good throughput, short data com- munication
delay, modularity, good fault tolerance and diameter vulnerability
correspond to properties of the underlying graphs of networks,
including large number of vertices, small diameter, high
connectivity and overall balance (or regularity) of the graph or
digraph. The ¯rst part of this thesis deals with the issue of
interconnection networks ad- dressing system. From graph theory
point of view, this issue is mainly related to a graph labeling. We
investigate a special family of graph labeling, namely antimagic
labeling of a class of disconnected graphs. We present new results
in super (a; d)-edge antimagic total labeling for disjoint union of
multiple copies of special families of graphs. The second part of
this thesis deals with the issue of regularity of digraphs with the
number of vertices close to the upper bound, called the Moore bound,
which is unobtainable for most values of out-degree and diameter.
Regularity of the underlying graph of a network is often considered
to be essential since the °ow of messages and exchange of data
between processing elements will be on average faster if there is a
similar number of interconnections coming in and going out of each
processing element. This means that the in-degree and out-degree of
each processing element must be the same or almost the same. Our new
results show that digraphs of order two less than Moore bound are
either diregular or almost diregular. | en_US |
