1. Prof. Narsingh Deo
Millican Chair Professor
Director, Center for Parallel Computation
University of Central Florida,
AN INDIAN MATHEMATICIAN
2. Narsingh Deo holds the Charles N. Millican Eminent Scholar’s Chair in
Computer Science and is the Director of the Center for Parallel
Computation at University of Central Florida, Orlando. Prior to this, he was a
Professor of Computer Science at Washington State University, where he
also served as the department chair. Before that he was a Professor of
Electrical Engineering and Computer Science at the Indian Institute of
Technology, Kanpur, and a Member of Technical Staff at Jet Propulsion
Laboratory. Recently he was elected as one of the fellows of the AAAS. He
has a Ph.D. from Northwestern University, an MS from Caltech and an
undergraduate degree from Indian Institute of Science—all in Electrical
Engineering.
He has held Visiting professorships at numerous institutions—including
at the University of Illinois, Urbana; University of Nebraska, Lincoln; Indian
Institute of Science, Bangalore; and IBM's T. J. Watson Research Center;
ETH, Zurich; University of Sao Paulo, Brazil; Oak Ridge National Lab.;
Australian National University, Canberra; Chuo University, Tokyo; Monash
University, Melbourne, Australia; and IIT/ Kharagpur.
3. A Fellow of IEEE, a Fellow of the ACM, and Fellow of the ICA, Dr.
Deo has authored four books in computer science (which have been
translated into several languages, including Russian, Polish, and
Japanese) and over 200 refereed research papers. He holds a
number of patents in computer hardware and is a recipient of NASA's
Apollo Achievement Award. Among his other awards are: Gold Medal
of Patna University; Drake Scholar at Cal Tech; Governor's Award for
Outstanding Contribution to High Tech Research in Florida (1989);
UCF's Distinguished Researcher Award-89; UCF's Professorial
Excellence Program Award (1997); UCF's Teaching Incentive
Program Award (1999); and UCF's Excellence in Graduate Teaching
Award (2001). He has served as an editor/guest editor for various
journals--including the IEEE Trans. on Circuits & Systems and the
Journal for Parallel and Distributed Computing. At present he is on
the Editorial Boards for The Journal of Supercomputing, and the VLSI
Design. He is currently the President of the Forum for
Interdisciplinary Mathematics. His research interests include parallel
algorithms and parallel data structures, network optimization
algorithms, combinatorial computing, complex networks, and graph
theory.
4.
5. HIS CONTRIBUTION:
Graph theory was born in 1736 with EULER’S paper in which he
solved the KONIGSBERG BRIDGE PROBLEM. The fertile period
was followed by half a century of relative inactivity. The past 30
years has been a period of intense activity in graph theory both pure
and applied. A great deal of research has been done and is being
done in this area by Dr. NARSINGH DEO.
WHAT IS GRAPH:
A graph is G=(V,E) consists of a set of objects V=(v1,v2,v3….) called
vertices and another set E=(e1,e2,e3…..) whose elements are called
edges. Each edge ek identified with unordered pair of vertices where
vi, vj are called end vertices. An edge having same vertex ,both its
end vertices , is called self loop. More than one edge associated with
a given pair of vertices referred to as parallel edges.
6. In drawing a graph it is immaterial whether lines are drawn straight or
curved. Graph is also called linear complex, 1-complex or 1-
dimensional complex.
Vertex referred as node, junction, point 0-cell or 0-simplex
Edges referred as branch, line, element, 1-cell or 1-simplex
APPLICATIONS OF GRAPH:
Graph theory has very wide range of applications in engineering, in
physical, in social and biological sciences, in linguistics and in
numerous other areas.
EX: 1) Konigsberg Bridge problem
2) Utilities problem
3) Electric network problem
4)Seating arrangement problem
8. In mathematics, a hypergraph is a generalization of a graph in which
an edge can connect any number of vertices.Formally, a hypergraph is
a pair where is a set of elements called nodes or vertices, and is a
set of non-empty subsets of called hyperedges or edges..
While graph edges are pairs of nodes, hyperedges are arbitrary sets of
nodes, and can therefore contain an arbitrary number of nodes.
However, it is often desirable to study hypergraphs where all
hyperedges have the same cardinality.A k-uniform hypergraph is a
hypergraph such that all its hyperedges have size k. (In other words, it is
a collection of sets of size k.) So a 2-uniform hypergraph is a graph, a 3-
uniform hypergraph is a collection of unordered triples, and so on.
A hypergraph is also called a set system or a family of sets drawn
from the universal set X. The difference between a set system and a
hypergraph (which is not well defined) is in the questions being asked.
Hypergraph theory tends to concern questions similar to those of graph
theory, such as connectivity ,while the theory of set systems tends to
ask non-graph-theoretical questions, such as those of Sperner theory.
9. There are variant definitions; sometimes edges must not be
empty, and sometimes multiple edges, with the same set of
nodes, are allowed.
Hypergraphs can be viewed as incidence structure. In
particular, there is "incidence graph" or “Levi graph“.
Hypergraphs have many other names. In computational
geometry, a hypergraph may sometimes be called a range
space and then the hyperedges are called ranges. In
cooperative game theory, hypergraphs are called simple
games (voting games); this notion is applied to solve
problems in social choice theory.
Special kinds of hypergraphs include, besides k-uniform
,clutters, where no edge appears as a subset of another edge;
and abstract simplicial complexs, which contain all subsets
of every edge.
The collection of hypergraphs is a category with hypergraph.
