Jasintha Quadras

Embedding of cycles and wheels into arbitrary trees

We estimate and characterize the edge congestion-sum measure for embeddings of various graphs such as cycles, wheels, and generalized wheels into arbitrary trees. All embedding algorithms apply an interesting general technique based on the consecutive label property. Our algorithms produce optimal values of sum of dilations and sum of edge-congestions in linear time.

Analytical expressions for Wiener indices of n-circumscribed peri-condensed benzenoid graphs

We have employed cut axes and vertex partitioning (I-partition) methods to obtain exact analytical expressions for Wiener indices of n-circumscribed peri-condensed benezenoid graphs as a function of n, the order of circumscribing. Such expressions have not been obtained before for nth order circumscribing of peri-condensed benzenoid graphs with the exception of n-Circum-coronene which becomes a honeycomb lattice as n goes to infinity. The Wiener indices of these n-circum peri-condensed benzenoids are found to be polynomials of degree 5. Such expressions can be critical in topological characterization of peri-condensed benzenoid sheets of any order of circumscribing. A number of examples are provided ranging from Circum-polyacenes, Circum-ovalenes, Circum-pyrenes to more complex Circum-peri-condensed graphs of wide ranging complexities.

Linear layout of locally twisted cubes

ABSTRACT The hypercube network is one of the most popular parallel computing networks since it has a simple structure and is easy to implement. The locally twisted cube is a newly introduced variant of the hypercube which has the same number of nodes and same number of connections per node as the hypercube, but has only half the diameter and better graph embedding capability as compared to hypercube. In this paper, we show that an n-dimensional locally twisted cube is constructed by forming a matching between the nodes of two disjoint copies of an -dimensional hypercube. In addition, we embed the locally twisted cube into path with minimum layout.

Embedding hypercubes and folded hypercubes onto Cartesian product of certain trees

The hypercube network is one of the most popular interconnection networks since it has simple structure and is easy to implement. The folded hypercube is an important variation of the hypercube. Interconnection networks play a major role in the performance of distributed memory multiprocessors and the one primary concern for choosing an appropriate interconnection network is the graph embedding ability. A graph embedding of a guest graph G into a host graph H is an injective map on the vertices such that each edge of G is mapped into a path of H . The wirelength of this embedding is defined to be the sum of the lengths of the paths corresponding to the edges of G . In this paper we embed hypercube and folded hypercube onto Cartesian product of trees such as 1-rooted complete binary tree and path, sibling tree and path to minimize the wirelength.

Embedding of the Folded Hypercubes into Tori

One of the most popular variants of hypercube network is the folded hypercube which can be constructed by adding a link to every pair of nodes with complementary addresses. The folded hypercube has been shown to be able to improve the system’s performance over a regular hypercube in many measurements. The family of torus is also one of the most popular interconnection networks due to its desirable properties such as regular structure, ease of implementation and good scalability. This paper is on the embedding of folded hypercube network into a family of torus whose exact wirelength is computed using the Congestion lemma and Partition lemma.

Domination in certain chemical graphs

Domination theory is required for encryption of binary string into a DNA sequence. A dominating set of a graph

Embedding of hypercubes into sibling trees

G=(V,E)

Biclique Cover of Complete Graph K n and Honeycomb Network HC ( n )

G=(V,E) is a subset