Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

The Transmission Lemma from Rajasingh et al. (2016) is extended to the General Transmission Lemma. It gives a formula for the transmission of a vertex u as a function of a collection of edge cuts and a u-routing that uniformly intersects the edge cuts. The applicability of the General Transmission Lemma is demonstrated by computing the Wiener complexity of triangular grid networks. © 2018 Elsevier Inc.

World University root node

VIT Unitversity

Mathematics

School of Advanced Sciences

Chennai Campus

Department of Design and Automation

School of Mechanical Engineering

Vellore Campus

Applied Mathematics and Computation

General Transmission Lemma and Wiener complexity of triangular grids

Wiener index of a graph $G$ is defined as $W(G) = frac 12 sum {u,v in V(G)}

The Computer Journal

Transmission in Butterfly Networks

The dilation of an embedding is defined as the maximum distance between pairs of vertices of host graph that are images of adjacent vertices of guest graph. An embedding with a long dilation faces many problems, such as long communication delay, coupling problems and the existence of different types of uncontrolled noise. In this paper, we compute the minimum dilation of embedding circulant networks into butterfly and benes networks. © Springer International Publishing Switzerland 2015.

Department of General Management

VIT Business School

Lecture Notes in Computer Science Combinatorial Algorithms

Embedding Circulant Networks into Butterfly and Benes Networks

Graph embedding problems have gained importance in the field of interconnection networks for parallel computer architectures. Interconnection networks provide an effective mechanism for exchanging data between processors in a parallel computing system. In this paper, we embed the rooted hypertree RHT(r) into r-dimensional hypercube Qr with dilation 2, r ≥ 2. Also, we compute the exact wirelength of the embedding of the r-dimensional hypercube Qr into the rooted hypertree RHT(r), r ≥ 2. © Journal of Graph Algorithms and Applications.

Journal of Graph Algorithms and Applications

Embeddings Between Hypercubes andHypertrees

The engineering of molecular products needs to be carried out by robotic devices, which have been termed nanorobots. A nanorobot architecture is used for biomedical applications in nanomedicine. A kekule structure in a molecular graph is nothing but a perfect matching in the graph. The minimum number of kekule structures that cover the edge set of a molecular graph G is known as the excessive index of G. The excessive index has been known to be a powerful tool for scheduling in the field of nanomedicine and simulation of nanoparticle structures. In this paper we determine the excessive index for armchair carbon nanotube, TUC4C8(S) nanotube and V -phenylenic nanotube. Copyright © 2014 American Scientific Publishers All rights reserved.

Journal of Computational and Theoretical Nanoscience

Excessive Index of Certain Nanotubes

Distance properties of molecular graphs form an important topic in chemical graph theory. The Padmakar-Ivan (PI) index of a graph G is the sum over all edges uv of G of the number of edges which are not equidistant from u and v and the Szeged (Sz) index of a graph G is the sum over all edges uv of G of the number of vertices which are not equidistant from u and v. In this paper we evolve an efficient method to calculate the PI index and Szeged index of pericondensed benzenoid graphs (r l), r l = 1 without using distance matrix. We also provide an Or l-linear time algorithm to compute the same. © 2014 American Scientific Publishers.

A New Technique to Compute Padmakar-Ivan Index and Szeged Index of Pericondensed Benzenoid Graphs

Dendrimers are recognized as one of the major commercially available nanoscale building blocks, large and complex molecules with well defined chemical structure. The nanostar dendrimer is a part of a new group of macroparticles that appear to be photon funnels just like artificial antennas. The total-Szeged index of a molecular graph G is defined as the sum of products tu(e) tv (e) over all edges e = (u. v) of G, where t u(e) is the number of vertices and edges of G whose distance to vertex u is smaller than the distance to vertex v, and where tv (e) is defined analogously. The aim of this paper is to compute the total-Szeged index of nanostar dendrimer NSC5C6. Copyright © 2014 American Scientific Publishers All rights reserved.

Computing Total-Szeged Index of Nanostar Dendrimer NSC5 C6

Distance properties of molecular graphs form an important topic in chemical graph theory. The Wiener index of a graph G is defined as the sum of all distances between distinct vertices of G. A lot of research has been devoted to finding Wiener index by brute force method. In this paper we develop a method to compute the Wiener index of certain chemical graphs without using distance matrix. Copyright © 2013 American Scientific Publishers All rights reserved.

Department of Mathematics

A New Approach to Compute Wiener Index

The structural formulae of chemical compounds are molecular graphs where vertices represent atoms and edges represent chemical bonds. A kekule structure in a molecular graph is nothing but a perfect matching in the graph. The minimum number of kekule structures that cover the edge set of a molecular graph G is known as the excessive index of G. In this paper we determine the excessive index of the unit cell representation of sodium chloride and 3-D mesh networks representing oxides and selenides of certain chemical compounds. Further we determine the excessive index of hexagonal networks. © 2013 Academic Publications, Ltd.

International Journal of Pure and Apllied Mathematics

EXCESSIVE INDEX OF CERTAIN CHEMICAL STRUCTURES

The total-Szeged index of a molecular graph G is defined as the sum of products tu(e)tv(e) over all edges e = (u, v) of G, where tu(e) is the number of vertices and edges of G whose distance to vertex u is smaller than the distance to vertex v, and where tv(e) is defined analogously. The aim of this paper is to compute the total-Szeged index of C4-nanotubes, C4-nanotori and two types of dendrimer nanostars. Copyright © 2013 American Scientific Publishers.

Total-Szeged Index of C4-Nanotubes, C4-Nanotori and Dendrimer Nanostars

In the present study, active fractions of the methanolic extract of Xanthium strumarium (XS) showing potent cytotoxicity were determined using microculture tetrazolium (MTT) and sulforhodamine B (SRB) assays in selected cancer cell lines. The active fractions viz., chloroform soluble fraction of root (CEXSR), hexane soluble fraction of leaf (HEXSL), hexane soluble fraction of fruits (HEXSF) and chloroform soluble fraction of fruits (CEXSF) of XS were tested in transplantable animal tumor models for their antitumor potential. Dalton's ascitic lymphoma (DLA) cells were used to induce solid and liquid (ascites) tumor in mice. The tumor bearing animals were treated with active fractions at two dose levels (100 and 200 mg/kg). The antitumor activities of the active fractions in tumor bearing animals were monitored with parameters such as body weight and increase in life-span as well as biochemical and hematological modalities (in the case of liquid tumor). Tumor incidence and tumor volume were the parameters monitored in the case of the solid tumor model. The results were analyzed by one-way ANOVA followed by Tukey's post hoc test. The extracts were found to increase the life-span of tumor bearing animals and restore the altered hematological and biochemical parameters significantly.

The American Journal of Chinese Medicine

Preliminary Evaluation of In Vitro Cytotoxicity and In Vivo Antitumor Activity of Xanthium strumarium in Transplantable Tumors in Mice

Graph embedding has been known as a powerful tool for implementation of parallel algorithms and simulation of interconnection networks. In this paper, we introduce a technique to obtain a lower bound for the dilation of an embedding. Moreover, we give algorithms for embedding variants of hypercubes with dilation 2 proving that the lower bound obtained is sharp. Further, we compute the exact wirelength of embedding folded hypercubes and augmented cubes into hypercubes.