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- Amitava Bhattacharya, Gurusamy Rengasamy Vijayakumar
- Discussiones Mathematicae Graph Theory
- 2002

Let G be a graph with ∆(G) > 1. It can be shown that the domination number of the graph obtained from G by subdividing every edge exactly once is more than that of G. So, let ξ(G) be the least number of edges such that subdividing each of these edges exactly once results in a graph whose domination number is more than that of G. The parameter ξ(G) is called… (More)

We settle affirmatively a conjecture posed in [S. some subsets of a set X are assigned injectively to all vertices of a complete bipartite graph G such that the collection of all sets, each of which is the symmetric difference of the sets assigned to the ends of some edge, is the set of all nonempty subsets of X , then G is a star. Infinite graphs and… (More)

- M Venkataravanappa, H Nagabhushana, +4 authors Udayabhanu
- Ultrasonics sonochemistry
- 2016

This paper reports for the first time ultrasound, EGCG assisted synthesis of pure and Eu(3+) (1-5mol%) activated Ca2SiO4 nanophosphors having self-assembled superstructures with high purity. The shape, size and morphology of the product were tuned by controlling influential parameters. It was found that morphology was highly dependent on EGCG concentration,… (More)

- M Venkataravanappa, H Nagabhushana, B Daruka Prasad, G P Darshan, R B Basavaraj, G R Vijayakumar
- Ultrasonics sonochemistry
- 2017

A novel Sr2SiO4:Eu (1-5mol %) superstructures (SS) were synthesized using bio-sacrificial A.V. gel assisted ultrasound method. Powder X-ray diffraction patterns confirmed the presence of both α and β phase formation. It was evident that the morphological growth was highly reliant on A.V. gel concentration, sonication time, pH and sonication power. The… (More)

A root system in which all roots have same norm is known as a simply laced root system. We present a simple method of classifying all simply laced root systems.

- Gurusamy Rengasamy Vijayakumar
- Discussiones Mathematicae Graph Theory
- 2010

An injective map from the vertex set of a graph G—its order may not be finite—to the set of all natural numbers is called an arithmetic (a geometric) labeling of G if the map from the edge set which assigns to each edge the sum (product) of the numbers assigned to its ends by the former map, is injective and the range of the latter map forms an arithmetic… (More)

- Gurusamy Rengasamy Vijayakumar
- Discrete Mathematics
- 2015

- Gurusamy Rengasamy Vijayakumar
- Discussiones Mathematicae Graph Theory
- 2013

The infimum of the least eigenvalues of all finite induced subgraphs of an infinite graph is defined to be its least eigenvalue. the class of all finite graphs whose least eigenvalues −2 has been classified: (1) If a (finite) graph is connected and its least eigenvalue is at least −2, then either it is a generalized line graph or it is represented by the… (More)

- R B Basavaraj, H Nagabhushana, B Daruka Prasad, G R Vijayakumar
- Ultrasonics sonochemistry
- 2017

The cationic surfactants assisted ultrasound route was used to prepare Dy(3+) doped Zn2SiO4 nanophosphors. The final products were characterized by powder X-ray diffraction (PXRD), ultraviolet visible spectroscopy, scanning electron microscopy, transmission electron microscopy and photoluminescence. Orthorhombic phase of Zn2SiO4:Dy(3+) (JCPDS card No.… (More)

- Gurusamy Rengasamy Vijayakumar
- Discussiones Mathematicae Graph Theory
- 2008

In this note we prove that {0, 1, √ 2, √ 3, 2} is the set of all real numbers such that the following holds: every tree having an eigenvalue which is larger than has a subtree whose largest eigenvalue is. For terminology and notation, we follow [8]. The path with n vertices and the star with n edges are denoted by P n and K 1,n , respectively. The largest… (More)