Micheal Arockiaraj

Embedding hypercubes into cylinders, snakes and caterpillars for minimizing wirelength

We consider the problem of embedding hypercubes into cylinders to minimize the wirelength. Further, we show that the edge isoperimetric problem solves the wirelength problem of regular graphs and, in particular, hypercubes into triangular snakes and caterpillars.

Embeddings of circulant networks

In this paper we solve the edge isoperimetric problem for circulant networks and consider the problem of embedding circulant networks into various graphs such as arbitrary trees, cycles, certain multicyclic graphs and ladders to yield the minimum wirelength.

Wirelength of hypercubes into certain trees

A lot of research has been devoted to finding efficient embedding of trees into hypercubes. On the other hand, in this paper, we consider the problem of embedding hypercubes into k-rooted complete binary trees, k-rooted sibling trees, binomial trees and certain classes of caterpillars to minimize the wirelength.

Wirelength of 1-fault hamiltonian graphs into wheels and fans

In this paper we obtain a fundamental result to find the exact wirelength of 1-fault hamiltonian graphs into wheels and fans. Using this result we compute the exact wirelength of circulant graphs, generalized Petersen graphs, augmented cubes, crossed cubes, Mobius cubes, locally twisted cubes, twisted cubes, twisted n-cubes, generalized twisted cubes, hierarchical cubic networks, alternating group graphs, arrangement graphs and tori into wheels and fans. In addition, we find the exact wirelength of hypercubes, folded hypercubes, shuffle cubes, cube connected cycles, cyclic-cubes, wrapped butterfly networks and star graphs into fans.

Vertex cut method for degree and distance-based topological indices and its applications to silicate networks

We have developed rigorous mathematical and computational techniques to obtain exact analytic expressions for a number of degree and distance-based topological indices of inorganic chemical networks and nanomaterials which are newly emerging areas of reticular chemistry. Derivations of these degree and distance-based topological indices of such chemical structures fall under a larger family of partial cubes for which only limited information is currently available. In the present study this gap is filled by developing a new method based on vertex decomposition and computing the degree and distance-based topological indices for polymeric chains, cyclic and double chain silicates, silicate and oxide networks as a function of n, the order of circumscribing.

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.

Analytical expressions for topological properties of polycyclic benzenoid networks

Quantitative structure‐activity and structure‐property relationships of complex polycyclic benzenoid networks require expressions for the topological properties of these networks. Structure‐based topological indices of these networks enable prediction of chemical properties and the bioactivities of these compounds through quantitative structure‐activity and structure‐property relationships methods. We consider a number of infinite convex benzenoid networks that include polyacene, parallelogram, trapezium, triangular, bitrapezium, and circumcorone series benzenoid networks. For all such networks, we compute analytical expressions for both vertex‐degree and edge‐based topological indices such as edge‐Wiener, vertex‐edge Wiener, vertex‐Szeged, edge‐Szeged, edge‐vertex Szeged, total‐Szeged, Padmakar‐Ivan, Schultz, Gutman, Randić, generalized Randić, reciprocal Randić, reduced reciprocal Randić, first Zagreb, second Zagreb, reduced second Zagreb, hyper Zagreb, augmented Zagreb, atom‐bond connectivity, harmonic, sum‐connectivity, and geometric‐arithmetic indices. In addition we have obtained expressions for these topological indices for 3 types of parallelogram‐like polycyclic benzenoid networks.

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.

Topological Indices and Their Applications to Circumcised Donut Benzenoid Systems, Kekulenes and Drugs

ABSTRACT This paper describes a new technique to compute topological indices of donut benzenoids and Kekulenes with applications to drugs by dissecting the original topological network into smaller strength-weighted quotient graphs relative to the transitive closure of the Djokovi–Winkler relation. We have applied this technique to a series of donut benzenoid graphs obtained by circumcising at least two internal hexagons from parent benzenoid graphs. Such donut coronoid graph finds significant applications in emerging chemical materials of importance to synthetic organic chemistry and drug industry. It comprised of donut coronoid structures such as Kekulenes and related circumscribed structures where a number of graph-theoretical based techniques, such as resonance theory and Clar’s sextets. In this work, we have computed a number of topological indices of these donut coronoid systems such as the Wiener index, variants of Szeged, Schultz and Gutman indices.

Optimal Embedding of Locally Twisted Cubes into Grids

The hypercube has been used in numerous problems related to interconnection networks due to its simple structure and communication properties. The locally twisted cube is an important class of hypercube variants with the same number of nodes and connections per node, but has only half the diameter and better graph embedding capability as compared to its counterpart. The embedding problem plays a significant role in parallel and distributed systems. In this paper we devise an optimal embedding of the n-dimensional locally twisted cube onto a grid network.