http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
Pair Difference Cordial Graphs Obtained From The Wheels and The Paths
R. Ponraj,A. Gayathri,S. Somasundaram 한국전산응용수학회 2021 Journal of Applied and Pure Mathematics Vol.3 No.3
Let G = (V, E) be a $(p,q)$ graph. Define \rho = \begin{cases}\frac{p}{2} ,& \text{if $p$ is even}\frac{p-1}{2} ,& \text{if $p$ is odd}\end{cases} and L = \{\pm1 ,\pm2, \pm3 , \cdots ,\pm\rho\} called the set of labels. Consider a mapping f : V \longrightarrow L by assigning different labels in L to the different elements of V when p is even and different labels in L to p-1 elements of V and repeating a label for the remaining one vertex when p is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge uv of G there exists a labeling \left|f(u) - f(v)\right| such that \left|\Delta_{f_1} - \Delta_{f_1^c}\right| \leq 1, where \Delta_{f_1} and \Delta_{f_1^c} respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate the pair difference cordial labeling behavior of some wheel and path related graphs.
Pair difference cordiality of some special graphs
R. Ponraj,A. Gayathri,S. Somasundaram 한국전산응용수학회 2021 Journal of Applied and Pure Mathematics Vol.3 No.5
Let G = (V, E) be a (p,q) graph. Define \begin{equation*}\rho =\begin{cases}\frac{p}{2} ,& \text{if p is even} \frac{p-1}{2} ,& \text{if p is odd}\end{cases} \end{equation*} and L = \{\pm1 ,\pm2, \pm3 , \cdots ,\pm\rho\} called the set of labels. Consider a mapping f : V \longrightarrow L by assigning different labels in L to the different elements of V when p is even and different labels in L to p-1 elements of V and repeating a label for the remaining one vertex when p is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge uv of G there exists a labeling \left|f(u) - f(v)\right| such that \left|\Delta_{f_1} - \Delta_{f_1^c}\right| \leq 1, where \Delta_{f_1} and \Delta_{f_1^c} respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate pair difference cordial labeling behavior of some special graphs like jelly fish, jewel graph, kayak padal graph, theta graph, bamboo tree, and olive tree.
Pair difference cordial labeling of Petersen graphs P(n,k)
R. Ponraj,A. Gayathri,S. Somasundaram 한국전산응용수학회 2023 Journal of Applied and Pure Mathematics Vol.5 No.1
Let $G = (V, E)$ be a $(p,q)$ graph. Define \begin{equation*} \rho = \begin{cases} \frac{p}{2} ,& \text{if $p$ is even}\\ \frac{p-1}{2} ,& \text{if $p$ is odd}\\ \end{cases} \end{equation*}\\ and $L = \{\pm1 ,\pm2, \pm3 , \cdots ,\pm\rho\}$ called the set of labels.\\ \noindent Consider a mapping $f : V \longrightarrow L$ by assigning different labels in L to the different elements of V when p is even and different labels in L to p-1 elements of V and repeating a label for the remaining one vertex when $p$ is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge $uv$ of $G$ there exists a labeling $\left|f(u) - f(v)\right|$ such that $\left|\Delta_{f_1} - \Delta_{f_1^c}\right| \leq 1$, where $\Delta_{f_1}$ and $\Delta_{f_1^c}$ respectively denote the number of edges labeled with $1$ and number of edges not labeled with $1$. A graph $G$ for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate pair difference cordial labeling behaviour of Petersen graphs $P(n,k)$ like $P(n,2), P(n,3),P(n,4)$.
PAIR DIFFERENCE CORDIAL LABELING OF PETERSEN GRAPHS P(n, k)
R. PONRAJ,A. GAYATHRI,S. SOMASUNDARAM The Korean Society for Computational and Applied M 2023 Journal of applied and pure mathematics Vol.5 No.1/2
Let G = (V, E) be a (p, q) graph. Define $${\rho}=\{{\frac{2}{p}},\;{\text{{\qquad} if p is even}}\\{\frac{2}{p-1}},\;{{\text{if p is odd}}$$ and L = {±1, ±2, ±3, … , ±ρ} called the set of labels. Consider a mapping f : V ⟶ L by assigning different labels in L to the different elements of V when p is even and different labels in L to p-1 elements of V and repeating a label for the remaining one vertex when p is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge uv of G there exists a labeling |f(u) - f(v)| such that ${\mid}{\Delta}_{f_1}-{\Delta}_{f^c_1}{\mid}{\leq}1$, where ${\Delta}_{f_1}$ and ${\Delta}_{f^c_1}$ respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate pair difference cordial labeling behaviour of Petersen graphs P(n, k) like P(n, 2), P(n, 3), P(n, 4).
Pair Difference Cordiality of Certain Subdivision Graphs
R. Ponraj,A. Gayathri,S. Somasundaram 한국전산응용수학회 2024 Journal of applied mathematics & informatics Vol.42 No.1
\noindent Let $G = (V, E)$ be a $(p,q)$ graph.\\ Define \begin{equation*} \rho = \begin{cases} \frac{p}{2} ,& \text{if $p$ is even}\\ \frac{p-1}{2} ,& \text{if $p$ is odd}\\ \end{cases} \end{equation*}\\ and $L = \{\pm1 ,\pm2, \pm3 , \cdots ,\pm\rho\}$ called the set of labels.\\ \noindent Consider a mapping $f : V \longrightarrow L$ by assigning different labels in $L$ to the different elements of $V$ when $p$ is even and different labels in $L$ to $p-1$ elements of $V$ and repeating a label for the remaining one vertex when $p$ is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge $uv$ of $G$ there exists a labeling $\left|f(u) - f(v)\right|$ such that $\left|\Delta_{f_1} - \Delta_{f_1^c}\right| \leq 1$, where $\Delta_{f_1}$ and $\Delta_{f_1^c}$ respectively denote the number of edges labeled with $1$ and number of edges not labeled with $1$. A graph $G$ for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate the pair difference cordial labeling behavior of subdivision of some graphs.
Devi K. Gayathri,Mooventhan A.,Mangaiarkarasi N.,Manavalan N. 사단법인약침학회 2023 Journal of Acupuncture & Meridian Studies Vol.16 No.6
Iron deficiency anemia (IDA) is an important public health issue in India. This study was performed to determine the impact of acupuncture at the GB39, BL17, and LR13 points on hemoglobin levels, mean corpuscular volume (MCV), mean corpuscular hemoglobin (MCH), and red cell distribution width (RDW) in people with IDA. One hundred women with IDA were randomly allocated to the acupuncture group (AG) or placebo control group (PCG). For 30 minutes per day, daily for 2 weeks, the AG received acupuncture at GB39, BL17, and LR13, while the PCG received needling at non-acupuncture points. Outcomes were assessed before and after the intervention. We found a significant increase (p < 0.001) in hemoglobin level (AG 10.39-11.38 g/dl, effect size 0.785; PCG 10.58-10.40 g/dl, effect size 0.191), MCH (AG 25.69-27.50 fl, effect size 0.418; PCG 27.43-27.23 fl, effect size 0.058), and RDW (AG 15.12-16.41 fl, effect size 0.626; PCG 14.91-14.94 fl, effect size 0.017) in the AG compared to the PCG. Results suggest that needling at the GB39, BL17, and LR13 acupuncture points is more effective in treating people with IDA than needling at non-acupuncture points.
PAIR DIFFERENCE CORDIAL NUMBER OF A GRAPH
R. PONRAJ,A. GAYATHRI The Korean Society for Computational and Applied M 2024 Journal of applied and pure mathematics Vol.6 No.3
Let G be a (p, q) graph. Pair difference cordial number of a graph G is the least positive integer m such that G∪mK<sub>2</sub> is pair difference cordial. It is denoted by PDC<sub>𝜂</sub>(G). In this paper we find the pair difference cordial number of bistar, complete, helm, star, wheel.
Pair difference cordial number of a graph
R. Ponraj,A. Gayathri 한국전산응용수학회 2024 Journal of Applied and Pure Mathematics Vol.6 No.3
Let $G$ be a $(p,q)$ graph. Pair difference cordial number of a graph $G$ is the least positive integer $m$ such that $G \cup m K_2$ is pair difference cordial. It is denoted by $PDC_{\eta}(G)$. In this paper we find the pair difference cordial number of bistar, complete, helm, star, wheel.
Pair difference cordial labeling of m-copies of some graphs
R. Ponraj,A. Gayathri,S. Somasundaram 한국전산응용수학회 2022 Journal of Applied and Pure Mathematics Vol.4 No.5
In this paper we investigate the pair difference cordial labeling behaviour of $m-$ copies of $K_4$, subdivision of star, fan, comb graphs.