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- 저자 : R. Kala (검색결과 7 건)
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R. Ponraj,Rajpal Singh,R. Kala,S. Sathish Narayanan 한국전산응용수학회 2016 Journal of applied mathematics & informatics Vol.34 No.3
In this paper we introduce a new graph labeling called $k$-prime cordial labeling. Let $G$ be a $(p,q)$ graph and $2\leq p\leq k$. Let $f:V(G)\to\{1,2, \ldots, k\}$ be a map. For each edge $uv$, assign the label $\gcd {(f(u), f(v))}$. $f$ is called a $k$-prime cordial labeling of $G$ if $\left|v_{f}(i)-v_{f}(j)\right|\leq 1$, $i,j\in\{1,2,\ldots, k\}$ and $\left|e_{f}(0)-e_{f}(1)\right|\leq 1$ where $v_{f}(x)$ denotes the number of vertices labeled with $x$, $e_{f}(1)$ and $e_{f}(0)$ respectively denote the number of edges labeled with $1$ and not labeled with $1$. A graph with a $k$-prime cordial labeling is called a $k$-prime cordial graph. In this paper we investigate the $k$-prime cordial labeling behavior of a star and we have proved that every graph is a subgraph of a $k$-prime cordial graph. Also we investigate the $3$-prime cordial labeling behavior of path, cycle, complete graph, wheel, comb and some more standard graphs.
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SOME 4-TOTAL PRIME CORDIAL LABELING OF GRAPHS
R. Ponraj,J. Maruthamani,R. Kala 한국전산응용수학회 2019 Journal of applied mathematics & informatics Vol.37 No.1
Let G be a (p, q) graph. Let f : V (G) ! {1, 2, . . . , k} be a map where k 2 N and k > 1. For each edge uv, assign the label gcd(f(u), f(v)). f is called k-Total prime cordial labeling of G if tf (i) − tf (j) 1, i, j 2 {1, 2, · · · , k} where tf (x) denotes the total number of vertices and the edges labelled with x. A graph with a k-total prime cordial labeling is called k- total prime cordial graph. In this paper we investigate the 4-total prime cordial labeling of some graphs.
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4-total difference cordial labeling of some special graphs
R. Ponraj,S. Yesu Doss Philip,R. Kala 한국전산응용수학회 2022 Journal of Applied and Pure Mathematics Vol.4 No.1
Let G be a graph. Let f:V(G)\to\{0,1,2, \ldots, k-1\} be a map where k \in \mathbb{N} and k>1. For each edge uv, assign the label \left|f(u)-f(v)\right|. f is called k-total difference cordial labeling of G if \left|t_{df}(i)-t_{df}(j)\right|\leq 1, i,j \in \{0,1,2,\ldots,k-1\} where t_{df}(x) denotes the total number of vertices and the edges labeled with x. A graph with admits a k-total difference cordial labeling is called k-total difference cordial graphs. In this paper we investigate the 4-total difference cordial labeling behaviour of shell butterfly graph, Lilly graph, Shackle graphs etc..
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PONRAJ, R.,SINGH, RAJPAL,KALA, R.,NARAYANAN, S. SATHISH The Korean Society for Computational and Applied M 2016 Journal of applied mathematics & informatics Vol.34 No.3
In this paper we introduce a new graph labeling called k-prime cordial labeling. Let G be a (p, q) graph and 2 ≤ p ≤ k. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called a k-prime cordial labeling of G if |v<sub>f</sub> (i) − v<sub>f</sub> (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |e<sub>f</sub> (0) − e<sub>f</sub> (1)| ≤ 1 where v<sub>f</sub> (x) denotes the number of vertices labeled with x, e<sub>f</sub> (1) and e<sub>f</sub> (0) respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with a k-prime cordial labeling is called a k-prime cordial graph. In this paper we investigate the k-prime cordial labeling behavior of a star and we have proved that every graph is a subgraph of a k-prime cordial graph. Also we investigate the 3-prime cordial labeling behavior of path, cycle, complete graph, wheel, comb and some more standard graphs.
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SOME 4-TOTAL PRIME CORDIAL LABELING OF GRAPHS
PONRAJ, R.,MARUTHAMANI, J.,KALA, R. The Korean Society for Computational and Applied M 2019 Journal of applied mathematics & informatics Vol.37 No.1
Let G be a (p, q) graph. Let $f:V(G){\rightarrow}\{1,2,{\ldots},k\}$ be a map where $k{\in}{\mathbb{N}}$ and k > 1. For each edge uv, assign the label gcd(f(u), f(v)). f is called k-Total prime cordial labeling of G if ${\mid}t_f(i)-t_f(j){\mid}{\leq}1$, $i,j{\in}\{1,2,{\ldots},k\}$ where $t_f$(x) denotes the total number of vertices and the edges labelled with x. A graph with a k-total prime cordial labeling is called k-total prime cordial graph. In this paper we investigate the 4-total prime cordial labeling of some graphs.
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4-TOTAL DIFFERENCE CORDIAL LABELING OF SOME SPECIAL GRAPHS
PONRAJ, R.,PHILIP, S. YESU DOSS,KALA, R. The Korean Society for Computational and Applied M 2022 Journal of applied and pure mathematics Vol.4 No.1/2
Let G be a graph. Let f : V (G) → {0, 1, 2, …, k-1} be a map where k ∈ ℕ and k > 1. For each edge uv, assign the label |f(u) - f(v)|. f is called k-total difference cordial labeling of G if |t<sub>df</sub> (i) - t<sub>df</sub> (j) | ≤ 1, i, j ∈ {0, 1, 2, …, k - 1} where t<sub>df</sub> (x) denotes the total number of vertices and the edges labeled with x. A graph with admits a k-total difference cordial labeling is called k-total difference cordial graphs. In this paper we investigate the 4-total difference cordial labeling behaviour of shell butterfly graph, Lilly graph, Shackle graphs etc..
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K. Kala,M. Sundara Ganeasan,V. Balasubramani,J. Manovasuki,K. Valivittan,T.M. Sridhar,M.R. Kuppusamy 한양대학교 세라믹연구소 2020 Journal of Ceramic Processing Research Vol.21 No.2
Recent efforts towards the treatment of bone defects and diseases focus on the development of bone scaffolds. Bioceramicsprovide strength, osteoconductivity and also imparts flexibility and resorbability. In this study, the biodegradable compositeswere fabricated using bioactive nano Hydroxyapatite (n-HAP) and bioresorbable nano β-Tricalcium phosphate (n-β-TCP)taken in 1:1 proportion. The nano composite scaffolds were synthesized using PEG (Poly Ethylene Glycol) by wet precipitationmethod. XRD (X-ray diffraction) confirms the presence of crystalline structure of n-HAP and n-β-TCP within the lattice. FESEM (Field Emission Scanning Electron Microscopy) and EDS (Energy Dispersion X-ray Spectroscopy) confirms the microporous nature and the phase purity of the composite. Further, biochemical studies were carried out using MG-63 Osteoblastcell line to evaluate their sustainability after implantation. The viability of the cells and proliferation rate is evaluated using3-(4,5-dimethylthiazole-2-yl)-2,5-diphenyltetrazolium bromide (MTT) with different concentration and different incubationperiod. The ALP (Alkaline Phosphotase) test reveals that the composite favours bone regeneration through apatite layerformation. Further studies were carried out to explore the DPPH (1,1-diphenyl-2-picrylhydrazyl) activity on the compositesand results reveals that the composite have an ability to trap the free radicals in the biological surroundings. The antimicrobialstudies indicate that the composites shows no major inhibitory effects towards the most common bone affecting bacteriaStaphylococcus aureus. The studies indicate that the concentration range of the composite is ideal for bone growth and can beused as substituents in the scaffold synthesis for normal and cancerous patients.
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