Gurusamy Rengasamy Vijayakumar

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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)
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)
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)
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)
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)
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)
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)
Let G = (V, E) be a graph of order n and let D that for all v ∈ V, u∈ND(v) f (u) is a constant, called D-vertex magic constant. O'Neal and Slater have proved the uniqueness of the D-vertex magic constant by showing that it can be determined by the D-neighborhood fractional domination number of the graph. In this paper we give a simple and elegant proof of(More)
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