Volume 56 (2024)
Volume 55 (2023)
Volume 54 (2022)
Volume 53 (2021)
Volume 52 (2020)
Volume 51 (2019)
Volume 50 (2018)
Volume 49 (2017)
Volume 48 (2016)
Volume 47 (2016)
Volume 46 (2015)
Volume 45 (2014)
Volume 44 (2013)
Volume 43 (2009)
Volume 42 (2008)
Volume 41 (2007)
4-TOTAL MEAN CORDIAL LABELING OF SOME TREES

R Ponraj; S SUBBULAKSHMI

Volume 56, Issue 1 , August 2024, , Pages 44-54

https://doi.org/10.22059/jac.2024.360730.1200

Abstract
  Let G be a graph. Let f : V (G) → {0, 1, 2,... ,k − 1}be a function where k ∈ N and k > 1. For each edge uv, assign thelabel f (uv) = lf(u)+f(v)2m. f is called a k-total mean cordial labeling of G if |tmf (i) − tmf (j)| ≤ 1, for all i,j ∈ {0, 1, 2,... ,k − 1},where ...  Read More

$4$-total mean cordial labeling of spider graph

R Ponraj; S SUBBULAKSHMI; Prof.Dr M.Sivakumar

Volume 55, Issue 1 , June 2023, , Pages 1-9

https://doi.org/10.22059/jac.2023.92447

Abstract
  Let $G$ be a graph. Let $f:V\left(G\right)\rightarrow \left\{0,1,2,\ldots,k-1\right\}$ be a function where $k\in \mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $f\left(uv\right)=\left\lceil \frac{f\left(u\right)+f\left(v\right)}{2}\right\rceil$. $f$ is called a $k$-total mean cordial ...  Read More

Pair Difference Cordial Labeling of Double Alternate Snake Graphs

R Ponraj; A Gayathri

Volume 55, Issue 1 , June 2023, , Pages 67-77

https://doi.org/10.22059/jac.2023.92513

Abstract
  In this paper we investigate the pair difference cordial labeling behavior of double alternate triangular snake and double alternate quadrilatral snake graphs.  Read More

Pair Difference Cordial Labeling of $m-$ copies of Path, Cycle, Star, and Ladder Graphs

R Ponraj; A Gayathri; Prof.Dr M.Sivakumar

Volume 54, Issue 2 , December 2022, , Pages 37-47

https://doi.org/10.22059/jac.2022.90409

Abstract
  In this paper, we consider only finite, undirected, and simple graphs. The concept of cordial labeling was introduced by Cahit[4]. Different types of cordial-related labeling were studied in [1, 2, 3, 5, 16]. In a similar line, the notion of pair difference cordial labeling of a graph was introduced ...  Read More

Pair mean cordial labeling of graphs

R Ponraj; S Prabhu

Volume 54, Issue 1 , June 2022, , Pages 1-10

https://doi.org/10.22059/jac.2022.87392

Abstract
  In this paper, we introduce a new graph labeling called pair mean cordial labeling of graphs. Also, we investigate the pair mean cordiality of some graphs like path, cycle, complete graph, star, wheel, ladder, and comb.  Read More

$4$-total mean cordial labeling of union of some graphs with the complete bipartite graph $K_{2,n}$

R Ponraj; S SUBBULAKSHMI; S Somasundaram

Volume 54, Issue 1 , June 2022, , Pages 35-46

https://doi.org/10.22059/jac.2022.88026

Abstract
  Let $G$ be a graph. Let $f:V\left(G\right)\rightarrow \left\{0,1,2,\ldots,k-1\right\}$ be a function where $k\in \mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $f\left(uv\right)=\left\lceil \frac{f\left(u\right)+f\left(v\right)}{2}\right\rceil$. $f$ is called $k$-total mean cordial labeling ...  Read More

Pair difference cordial labeling of planar grid and mangolian tent

R Ponraj; A Gayathri; S Somasundaram

Volume 53, Issue 2 , December 2021, , Pages 47-56

https://doi.org/10.22059/jac.2021.85196

Abstract
   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 ...  Read More

$4$-total mean cordial labeling of special graphs

R Ponraj; S SUBBULAKSHMI; S Somasundaram

Volume 53, Issue 1 , June 2021, , Pages 13-22

https://doi.org/10.22059/jac.2021.81169

Abstract
  Let $G$ be a graph. Let $f:V\left(G\right)\rightarrow \left\{0,1,2,\ldots,k-1\right\}$ be a function where $k\in \mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $f\left(uv\right)=\left\lceil \frac{f\left(u\right)+f\left(v\right)}{2}\right\rceil$. $f$ is called $k$-total mean cordial labeling ...  Read More

An Alternative Proof for a Theorem of R.L. Graham Concerning CHEBYSHEV Polynomials

A.M.S.. Ramasamy; R Ponraj

Volume 53, Issue 1 , June 2021, , Pages 117-122

https://doi.org/10.22059/jac.2021.81593

Abstract
  In this paper, an alternative proof is provided for a theorem of R.L.Graham concerning Chebyshev polynomials.  While studying the properties of a double star, R.L.Graham [2] proved a theorem concerning Chebyshev polynomials of the first kind ${T_n (x)}$. The purpose of this paper is to provide an ...  Read More

Pair Difference Cordiality of Some Snake and Butterfly Graphs

R Ponraj; A Gayathri; S Somasundaram

Volume 53, Issue 1 , June 2021, , Pages 149-163

https://doi.org/10.22059/jac.2021.81649

Abstract
  \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 ...  Read More

$4$-total mean cordial labeling in subdivision graphs

R Ponraj; S SUBBULAKSHMI; S Somasundaram

Volume 52, Issue 2 , December 2020, , Pages 1-11

https://doi.org/10.22059/jac.2020.78640

Abstract
  Let $G$ be a graph. Let $f:V\left(G\right)\rightarrow \left\{0,1,2,\ldots,k-1\right\}$ be a function where $k\in \mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $f\left(uv\right)=\left\lceil \frac{f\left(u\right)+f\left(v\right)}{2}\right\rceil$.  $f$ is called $k$-total mean cordial ...  Read More

PD-prime cordial labeling of graphs

R Ponraj; S SUBBULAKSHMI; S Somasundaram

Volume 51, Issue 2 , December 2019, , Pages 1-7

https://doi.org/10.22059/jac.2019.75109

Abstract
  \vspace{0.2cm} Let $G$ be a graph and $f:V(G)\rightarrow \{1,2,3,.....\left|V(G)\right|\}$ be a bijection. Let $p_{uv}=f(u)f(v)$ and\\ $ d_{uv}= \begin{cases} \left[\frac{f(u)}{f(v)}\right] ~~if~~ f(u) \geq f(v)\\ \\ \left[\frac{f(v)}{f(u)}\right] ~~if~~ f(v) \geq f(u)\\ \end{cases} $\\ for all edge ...  Read More

$k$-Total difference cordial graphs

R Ponraj; S.Yesu Doss Philip; R Kala

Volume 51, Issue 1 , June 2019, , Pages 121-128

https://doi.org/10.22059/jac.2019.71773

Abstract
  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 a $k$-total difference cordial labeling of $G$ if $\left|t_{df}(i)-t_{df}(j)\right|\leq 1$, $i,j \in \{0,1,2, \ldots, ...  Read More

$4$-Total prime cordial labeling of some cycle related graphs

R Ponraj; J Maruthamani

Volume 50, issue 2 , December 2018, , Pages 49-57

https://doi.org/10.22059/jac.2018.69777

Abstract
  Let $G$ be a $(p,q)$ graph. Let $f:V(G)\to\{1,2, \ldots, k\}$ 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 $\left|t_{f}(i)-t_{f}(j)\right|\leq 1$, $i,j \in \{1,2, \cdots,k\}$ where $t_{f}(x)$ ...  Read More

$k$-Total prime cordial labeling of graphs

R Ponraj; J Maruthamani; R Kala

Volume 50, Issue 1 , June 2018, , Pages 143-149

https://doi.org/10.22059/jac.2018.68651

Abstract
  In this paper we introduce a new graph labeling method called $k$-Total prime cordial. Let $G$ be a $(p,q)$ graph. Let $f:V(G)\to\{1,2, \ldots, k\}$ 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 ...  Read More

k-Remainder Cordial Graphs

R. Ponraj; K. Annathurai; R. Kala

Volume 49, Issue 2 , December 2017, , Pages 41-52

https://doi.org/10.22059/jac.2017.7976

Abstract
  In this paper we generalize the remainder cordial labeling, called $k$-remainder cordial labeling and investigate the $4$-remainder cordial labeling behavior of certain graphs.  Read More

Remainder Cordial Labeling of Graphs

R. Ponraj; K. Annathurai; R. Kala

Volume 49, Issue 1 , June 2017, , Pages 17-30

https://doi.org/10.22059/jac.2017.7965

Abstract
  In this paper we introduce remainder cordial labeling of graphs. Let $G$ be a $(p,q)$ graph. Let $f:V(G)\rightarrow \{1,2,...,p\}$ be a $1-1$ map. For each edge $uv$ assign the label $r$ where $r$ is the remainder when $f(u)$ is divided by $f(v)$ or $f(v)$ is divided by $f(u)$ according as $f(u)\geq ...  Read More

A note on 3-Prime cordial graphs

R. Ponraj; Rajpal Singh; S. Sathish Narayanan

Volume 48, Issue 1 , December 2016, , Pages 45-55

https://doi.org/10.22059/jac.2016.7939

Abstract
  Let G be a (p, q) graph. 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 k-prime cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number ...  Read More

4-Prime cordiality of some classes of graphs

R. Ponraj; Rajpal Singh; S. Sathish Narayanan; A. M. S. Ramasamy

Volume 48, Issue 1 , December 2016, , Pages 69-79

https://doi.org/10.22059/jac.2016.7941

Abstract
  Let G be a (p, q) graph. 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 k-prime cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number ...  Read More

3-difference cordial labeling of some cycle related graphs

R. Ponraj; M. Maria Adaickalam

Volume 47, Issue 1 , June 2016, , Pages 1-10

https://doi.org/10.22059/jac.2016.7927

Abstract
  Let G be a (p, q) graph. Let k be an integer with 2 ≤ k ≤ p and f from V (G) to the set {1, 2, . . . , k} be a map. For each edge uv, assign the label |f(u) − f(v)|. The function f is called a k-difference cordial labeling of G if |νf (i) − vf (j)| ≤ 1 and ...  Read More

Further results on total mean cordial labeling of graphs

R. Ponraj; S. Sathish Narayanan

Volume 46, Issue 1 , December 2015, , Pages 73-83

https://doi.org/10.22059/jac.2015.7926

Abstract
  A graph G = (V,E) with p vertices and q edges is said to be a total mean cordial graph if there exists a function f : V (G) → {0, 1, 2} such that f(xy) = [(f(x)+f(y))/2] where x, y ∈ V (G), xy ∈ E(G), and the total number of 0, 1 and 2 are balanced. That is |evf (i) ...  Read More