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SECURE DOMINATION PARAMETERS OF HALIN GRAPH WITH PERFECT K-ARY TREE
R. ARASU,N. PARVATHI The Korean Society for Computational and Applied M 2023 Journal of applied mathematics & informatics Vol.41 No.4
Let G be a simple undirected graph. A planar graph known as a Halin graph(HG) is characterised by having three connected and pendent vertices of a tree that are connected by an outer cycle. A subset S of V is said to be a dominating set of the graph G if each vertex u that is part of V is dominated by at least one element v that is a part of S. The domination number of a graph is denoted by the γ(G), and it corresponds to the minimum size of a dominating set. A dominating set S is called a secure dominating set if for each v ∈ V\S there exists u ∈ S such that v is adjacent to u and S<sub>1</sub> = (S\{v}) ∪ {u} is a dominating set. The minimum cardinality of a secure dominating set of G is equal to the secure domination number γ<sub>s</sub>(G). In this article we found the secure domination number of Halin graph(HG) with perfet k-ary tree and also we determined secure domination of rooted product of special trees.
Nath Deena,Chakravarty Sujay,Deshpade U.P.,Arasu A.V. Thanikai,Baskaran R.,Shekar N.V. Chandra 한국물리학회 2022 Current Applied Physics Vol.34 No.-
In this work for the first time, we are reporting the unusual observation of the Kondo effect with the coexistence of room temperature ferromagnetism in AlN/Al/AlN trilayer thin film. The grown film shows resistivity minimum at a temperature of ~48K, which shifts to the lower temperature on the application of magnetic fields. After considering various possibilities for an upturn in resistivity, we found that the Kondo scattering is responsible for upturn at low temperature. The simultaneous presence of ferromagnetism and Kondo scattering is explained by spatial variation of nitrogen vacancy defects from the film surface to the Al sandwich layer. Furthermore, magneto-transport properties of the film measured at different temperature exhibits both negative and positive components described by localized magnetic moment model for the spin scattering of carriers and two-band model, respectively. This work provides insight into the novel co-existence of ferromagnetism and Kondo effect in crystalline AlN.
Yusser Al-Qazwini,A.S.M. Noor,P.T. Arasu,A.R. Sadrolhosseini 한국물리학회 2013 Current Applied Physics Vol.13 No.7
Finite-difference time domain (FDTD) method was used to investigate the performance of surface plasmon resonance (SPR)-based optical fiber sensors. The results show that the performance of the fiber sensor can be optimized by choosing a proper combination of metal layer thickness of 40-60 nm and residual cladding thickness of 400-500 nm. Furthermore, the roughness effect of the gold surface layering the fiber sensor is significant in rough surfaces when sigma rms is greater than 5 nm or correlation length is lower than 100 nm.