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

In this paper, we propose a new conjecture that the complete graph K4m+1 can be decomposed into copies of two arbitrary trees, each of size m, m≥ 1. To support this conjecture we prove that the complete graph K4cm+1 can be decomposed into copies of an arbitrary tree with m edges and copies of the graph H, where H is either a path with m edges or a star with m edges and where c is any positive integer. Further, we discuss related open problems. © 2021, The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature.

World University root node

Department of Mathematics

School of Advanced Sciences

Vellore Campus

Graphs and Combinatorics

Decomposition of Complete Graphs into Arbitrary Trees

A graceful labeling of a graph G with q edges is ail injection/: V(G)-? {0,1,2, • • • , q} with the property that the resulting edge labels are distinct, where an edge incident with vertices x and y is assigned the label |/(x)-/(y)|. The conjecture of TYuszczynski's states that all unicyclic graphs except the cycle Cn with n = 1 or 2(mod 4) are graceful. In this paper, we construct a graceful unicyclic graph G from every graceful tree T such that V(G) = V(T) and where the graceful labeling of G is derived from the graceful labeling of T. © 2020 Charles Babbage Research Centre. All rights reserved.

Ars Combinatoria

Generating graceful unicyclic graph from a given graceful tree

Acharya (1982) proved that every connected graph can be embedded in a graceful graph. The generalization of this result that, any set of graphs can be packed into a graceful graph was proved by Sethuraman and Elumalai (2005). Recently, Sethuraman et al. (2016) have shown that, every tree can be embedded in an graceful tree. Inspired by these fundamental structural properties of graceful graphs, in this paper, we prove that any acyclic graph can be embedded in an unicyclic graceful graph. This result is proved algorithmically by constructing graceful unicyclic graphs from a given acyclic graph. Our result strongly supports the Truszczynski’s Conjecture that “All unicyclic graphs except the cycle (Formula presented.) with (Formula presented.) or 2(mod 4) are graceful”. © 2018 Kalasalingam University. Published with license by Taylor & Francis Group, LLC.

Fulltext

AKCE International Journal of Graphs and Combinatorics

Generating graceful unicyclic graphs from a given forest

Frank Harary and Allen J. Schwenk have given a formula for counting the number of non-isomorphic caterpillars on n vertices with n > 3. Inspired by the formula of Frank Harary and Allen J. Schwenk, in this paper, we give a formula for counting the number of non-isomorphic caterpillars with the same degree sequence. © 2020 Charles Babbage Research Centre. All rights reserved.

Journal of Combinatorial Mathematics and Combinatorial Computing

Enumeration of caterpillars

Frank Harary and Allen J. Schwenk [The number of caterpillars, Discrete Mathematics, 6 (1973), 359-365] have given an elegant formula for counting the number of non-isomorphic caterpillars on n vertices with n ≥ 3. In this paper we provide an alternate simple proof for Frank Harary and Allen J. Schwenk formula using combination with repetition. © 2020 Author(s).

AIP Conference Proceedings

An alternate proof for counting the number of caterpillars

A facile microwave-assisted reaction was used to synthesize graphene oxide with cerium oxide nanoparticles (GO-CeO2 NPs) from water extracts of Moringa oleifera flower. The one step microwave synthesis treatment was used for reduction of ceria atom to cerium oxide nanoparticles along with the reduction of graphene oxide. The synthesized GO-CeO2 NPs were analysed by various analytical instrumentation techniques and we found the size of nanoparticles as 50 nm with a spherical shape. Further, the green synthesized GO-CeO2 NPs were employed as a catalyst to reduce 4-nitrophenol and achieved a degradation rate of 95.45%. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Department of Chemistry

Journal of Inorganic and Organometallic Polymers and Materials

Degradation Treatment of 4-Nitrophenol by Moringa oleifera Synthesised GO-CeO2 Nanoparticles as Catalyst

A graceful labeling of a graph G with n edges is an injection f:V(G)→{0,1,2,⋯,n} with the property that the resulting edge labels are also distinct, where an edge incident with vertices u and v is assigned the label |f(u)−f(v)|. A graph which admits a graceful labeling is called a graceful graph. In this paper, inspired by Koh [K.M. Koh, D.G. Rogers and T. Tan, Two theorems on graceful trees, Discrete Math., 25 (1979), 141–148] method, which combines a known graceful trees to obtain a larger graceful trees, we introduced a new method of combining graceful trees called recursive attachment method, and we show that the recursively attached tree Ti=Ti−1⊕TAi−1 is graceful, for i≥1, where T0 is a base tree which is taken as a caterpillar and TAi−1 is an attachment tree which taken as any caterpillar. Here Ti−1⊕TAi−1 represents a tree obtained by attaching a copy of TAi−1 at each vertex of degree at least two in Ti−1, for i≥1. Consequently the graceful tree conjecture is true for every recursively attached caterpillar tree Ti, for i≥1. © 2016 Elsevier B.V.

Electronic Notes in Discrete Mathematics

Generating Graceful Trees from Caterpillars by Recursive Attachment

The present study discusses the development of an algorithm to generate input files for quantum mechanical (QM) calculations from molecular dynamics (MD) trajectories of protein-carbohydrate complex simulations and QM optimization of binding-site residues of influenza hemagglutinin H1 along with its cell surface receptor sialyldisaccharides Neu5Acα(2→3)Gal (N23G) and Neu5Acα(2→6)Gal (N26G). Five frames from the local minima of MD trajectories were chosen for QM calculations. The geometry optimization was carried out by Gaussian09 software. The optimized geometries were analyzed, and the resultant ab initio molecular structures can be used for inhibitor design and therapeutics of influenza A virus. Copyright © 2015 Taylor & Francis Group, LLC.

Department Of Biotechnology

Department of Physics

Journal of Carbohydrate Chemistry

Geometry Optimization of Carbohydrate Binding Sites of Influenza: A Quantum Mechanical Approach

Galectins are β-galactoside binding proteins which have the ability to serve as potent antitumor, cancer biomarker, and induce tumor cell apoptosis. Agrocybe cylindracea galectin (ACG) is a fungal galectin which specifically recognizes α(2,3)-linked sialyllactose at the cell surface that plays extensive roles in the biological recognition processes. To investigate the change in glycan-binding specificity upon mutations, single point and double point site-directed in silico mutations are performed at the binding pocket of ACG. Molecular dynamics (MD) simulation studies are carried out for the wild-type (ACG) and single point (ACG1) and double point (ACG2) mutated ACGs to investigate the dynamics of substituted mutants and their interactions with the receptor sialyllactose. Plausible binding modes are proposed for galectin-sialylglycan complexes based on the analysis of hydrogen bonding interactions, total pair-wise interaction energy between the interacting binding site residues and sialyllactose and binding free energy of the complexes using molecular mechanics-Poisson-Boltzmann surface area. Our result shows that high contribution to the binding in different modes is due to the direct and water-mediated hydrogen bonds. The binding specificity of double point mutant Y59R/N140Q of ACG2 is found to be high, and it has 26 direct and water-mediated hydrogen bonds with a relatively low-binding free energy of -47.52 ± 5.2 kcal/mol. We also observe that the substituted mutant Arg59 is crucial for glycan-binding and for the preference of α(2,3)-linked sialyllactose at the binding pocket of ACG2 galectin. When compared with the wild-type and single point mutant, the double point mutant exhibits enhanced affinity towards α(2,3)-linked sialyllactose, which can be effectively used as a model for biological cell marker in cancer therapeutics. © 2015 John Wiley & Sons, Ltd.

Journal of Molecular Recognition

Theoretical investigation on the glycan-binding specificity of Agrocybe cylindracea galectin using molecular modeling and molecular dynamics simulation studies