• Title/Summary/Keyword: cordial labeling

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POWER CORDIAL GRAPHS

  • C.M. BARASARA;Y.B. THAKKAR
    • Journal of applied mathematics & informatics
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    • v.42 no.2
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    • pp.445-456
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    • 2024
  • A power cordial labeling of a graph G = (V (G), E(G)) is a bijection f : V (G) → {1, 2, ..., |V (G)|} such that an edge e = uv is assigned the label 1 if f(u) = (f(v))n or f(v) = (f(u))n, for some n ∈ ℕ ∪ {0} {0} and the label 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. In this paper, we study power cordial labeling and investigate power cordial labeling for some standard graph families.

On Prime Cordial Labeling of Graphs

  • Aljouiee, Abdullah
    • Kyungpook Mathematical Journal
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    • v.56 no.1
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    • pp.41-46
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    • 2016
  • A graph G of order n has prime cordial labeling if its vertices can be assigned the distinct labels 1, $2{\cdots}$, n such that if each edge xy in G is assigned the label 1 in case the labels of x and y are relatively prime and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. In this paper, we give a complete characterization of complete graphs which are prime cordial and we give a prime cordial labeling of the closed helm ${\bar{H}}_n$, and present a new way of prime cordial labeling of $P^2_n$. Finally we make a correction of the proof of Theorem 2.5 in [12].

SOME NEW RESULTS ON POWER CORDIAL LABELING

  • C.M. BARASARA;Y.B. THAKKAR
    • Journal of applied mathematics & informatics
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    • v.41 no.3
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    • pp.615-631
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    • 2023
  • A power cordial labeling of a graph G = (V (G), E(G)) is a bijection f : V (G) → {1, 2, ..., |V (G)|} such that an edge e = uv is assigned the label 1 if f(u) = (f(v))n or f(v) = (f(u))n, For some n ∈ ℕ ∪ {0} and the label 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. In this paper, we investigate power cordial labeling for helm graph, flower graph, gear graph, fan graph and jewel graph as well as larger graphs obtained from star and bistar using graph operations.

k-PRIME CORDIAL GRAPHS

  • PONRAJ, R.;SINGH, RAJPAL;KALA, R.;NARAYANAN, S. SATHISH
    • Journal of applied mathematics & informatics
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    • v.34 no.3_4
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    • pp.227-237
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    • 2016
  • 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 |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (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.

GROUP S3 MEAN CORDIAL LABELING FOR STAR RELATED GRAPHS

  • A. LOURDUSAMY;E. VERONISHA
    • Journal of applied mathematics & informatics
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    • v.41 no.2
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    • pp.321-330
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    • 2023
  • Let G = (V, E) be a graph. Consider the group S3. Let g : V (G) → S3 be a function. For each edge xy assign the label 1 if ${\lceil}{\frac{o(g(x))+o(g(y))}{2}}{\rceil}$ is odd or 0 otherwise. g is a group S3 mean cordial labeling if |vg(i) - vg(j)| ≤ 1 and |eg(0) - eg(1)| ≤ 1, where vg(i) and eg(y)denote the number of vertices labeled with an element i and number of edges labeled with y (y = 0, 1). The graph G with group S3 mean cordial labeling is called group S3 mean cordial graph. In this paper, we discuss group S3 mean cordial labeling for star related graphs.

PAIR MEAN CORDIAL LABELING OF SOME UNION OF GRAPHS

  • R. PONRAJ;S. PRABHU
    • Journal of Applied and Pure Mathematics
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    • v.6 no.1_2
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    • pp.55-69
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    • 2024
  • Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}=\{\array{{\frac{p}{2}} && p\;\text{is even} \\ {\frac{p-1}{2}} && p\;\text{is odd,}}$$ and M = {±1, ±2, … ± 𝜌} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M 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 mean cordial labeling if for each edge uv of G, there exists a labeling $\frac{{\lambda}(u)+{\lambda}(v)}{2}$ if λ(u) + λ(v) is even and $\frac{{\lambda}(u)+{\lambda}(v)+1}{2}$ if λ(u) + λ(v) is odd such that ${\mid}\bar{\mathbb{s}}_{{\lambda}_1}-\bar{\mathbb{s}}_{{\lambda}^c_1}{\mid}\,{\leq}\,1$ where $\bar{\mathbb{s}}_{{\lambda}_1}$ and $\bar{\mathbb{s}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G with a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling behavior of some union of graphs.

TOTAL MEAN CORDIAL LABELING OF SOME CYCLE RELATED GRAPHS

  • Ponraj, R.;Narayanan, S. Sathish
    • Journal of applied mathematics & informatics
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    • v.33 no.1_2
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    • pp.101-110
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    • 2015
  • A Total Mean Cordial labeling of a graph G = (V, E) is a function $f:V(G){\rightarrow}\{0,1,2\}$ such that $f(xy)={\Large\lceil}\frac{f(x)+f(y)}{2}{\Large\rceil}$ where $x,y{\in}V(G)$, $xy{\in}E(G)$, and the total number of 0, 1 and 2 are balanced. That is ${\mid}ev_f(i)-ev_f(j){\mid}{\leq}1$, $i,j{\in}\{0,1,2\}$ where $ev_f(x)$ denotes the total number of vertices and edges labeled with x (x = 0, 1, 2). If there is a total mean cordial labeling on a graph G, then we will call G is Total Mean Cordial. Here, We investigate the Total Mean Cordial labeling behaviour of prism, gear, helms.

SOME 4-TOTAL PRIME CORDIAL LABELING OF GRAPHS

  • PONRAJ, R.;MARUTHAMANI, J.;KALA, R.
    • Journal of applied mathematics & informatics
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    • v.37 no.1_2
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    • pp.149-156
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    • 2019
  • 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.

4-TOTAL DIFFERENCE CORDIAL LABELING OF SOME SPECIAL GRAPHS

  • PONRAJ, R.;PHILIP, S. YESU DOSS;KALA, R.
    • Journal of Applied and Pure Mathematics
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    • v.4 no.1_2
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    • pp.51-61
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    • 2022
  • 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 |tdf (i) - tdf (j) | ≤ 1, i, j ∈ {0, 1, 2, …, k - 1} where tdf (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..

GROUP S3 CORDIAL REMAINDER LABELING OF SUBDIVISION OF GRAPHS

  • LOURDUSAMY, A.;WENCY, S. JENIFER;PATRICK, F.
    • Journal of applied mathematics & informatics
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    • v.38 no.3_4
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    • pp.221-238
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    • 2020
  • Let G = (V (G), E(G)) be a graph and let g : V (G) → S3 be a function. For each edge xy assign the label r where r is the remainder when o(g(x)) is divided by o(g(y)) or o(g(y)) is divided by o(g(x)) according as o(g(x)) ≥ o(g(y)) or o(g(y)) ≥ o(g(x)). The function g is called a group S3 cordial remainder labeling of G if |vg(i)-vg(j)| ≤ 1 and |eg(1)-eg(0)| ≤ 1, where vg(j) denotes the number of vertices labeled with j and eg(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S3 cordial remainder labeling is called a group S3 cordial remainder graph. In this paper, we prove that subdivision of graphs admit a group S3 cordial remainder labeling.