• Title/Summary/Keyword: Graph Labeling

Search Result 73, Processing Time 0.028 seconds

On Prime Cordial Labeling of Graphs

  • Aljouiee, Abdullah
    • Kyungpook Mathematical Journal
    • /
    • v.56 no.1
    • /
    • pp.41-46
    • /
    • 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].

V-SUPER VERTEX OUT-MAGIC TOTAL LABELINGS OF DIGRAPHS

  • Devi, Guruvaiah Durga;Durga, Morekondan Subhash Raja;Marimuthu, Gurusamy Thevar
    • Communications of the Korean Mathematical Society
    • /
    • v.32 no.2
    • /
    • pp.435-445
    • /
    • 2017
  • Let D be a directed graph with p vertices and q arcs. A vertex out-magic total labeling is a bijection f from $V(D){\cup}A(D){\rightarrow}\{1,2,{\ldots},p+q\}$ with the property that for every $v{\in}V(D)$, $f(v)+\sum_{u{\in}O(v)}f((v,u))=k$, for some constant k. Such a labeling is called a V-super vertex out-magic total labeling (V-SVOMT labeling) if $f(V(D))=\{1,2,3,{\ldots},p\}$. A digraph D is called a V-super vertex out-magic total digraph (V-SVOMT digraph) if D admits a V-SVOMT labeling. In this paper, we provide a method to find the most vital nodes in a network by introducing the above labeling and we study the basic properties of such labelings for digraphs. In particular, we completely solve the problem of finding V-SVOMT labeling of generalized de Bruijn digraphs which are used in the interconnection network topologies.

A Study on the Voxel Coloring using Multi-variable Thresholding (다중 가변 문턱값을 이용한 복셀 칼라링 기법에 관한 연구)

  • Kim Hyo-Sung;Lee Sang-Wook;Nam Ki-Gon
    • Journal of the Korea Institute of Information and Communication Engineering
    • /
    • v.9 no.5
    • /
    • pp.1102-1110
    • /
    • 2005
  • In this paper, we proposed a advanced approach to resolve the trade-off problem for the threshold value determining the photo-consistency in the previous algorithms. The threshold value for the surface voxel is substituted the photo-consistency value of the inside voxel. As iterating the voxel coloring process, the threshold is approached to the optimal value for the individual surface voxel. we present an energy minimization formulation of the binary labeling problem that surface voxels classify into opacity or transparency. The energy formula consists of the data term and the smoothness term. As considering neighboring voxels in the labeling problem, the unevenness of reconstructed surface is reduced. The labeling whose energy is the global minimum can be computed using a graph cut.

The Fibonacci Edge Labelings on Fibonacci Trees (피보나치트리에서 피보나치 에지 번호매김방법)

  • Kim, Yong-Seok
    • Journal of KIISE:Computer Systems and Theory
    • /
    • v.36 no.6
    • /
    • pp.437-450
    • /
    • 2009
  • In this paper, we propose seven edge labeling methods. The methods produce three case of edge labels-sets of Fibonacci numbers {$F_k|k\;{\geq}\;2$}, {$F_{2k}|k\;{\geq}\;1$} and {$F_{3k+2}|k\;{\geq}\;0$}. When a sort of interconnection network, the circulant graph is designed, these edge labels are used for its jump sequence. As a result, the degree is due to the edge labels.

DISTANCE TWO LABELING ON THE SQUARE OF A CYCLE

  • ZHANG, XIAOLING
    • Korean Journal of Mathematics
    • /
    • v.23 no.4
    • /
    • pp.607-618
    • /
    • 2015
  • An L(2; 1)-labeling of a graph G is a function f from the vertex set V (G) to the set of all non-negative integers such that ${\mid}f(u)-f(v){\mid}{\geq}2$ if d(u, v) = 1 and ${\mid}f(u)-f(v){\mid}{\geq}1$ if d(u, v) = 2. The ${\lambda}$-number of G, denoted ${\lambda}(G)$, is the smallest number k such that G admits an L(2, 1)-labeling with $k=\max\{f(u){\mid}u{\in}V(G)\}$. In this paper, we consider the square of a cycle and provide exact value for its ${\lambda}$-number. In addition, we also completely determine its edge span.

REVERSE EDGE MAGIC LABELING OF CARTESIAN PRODUCT, UNIONS OF BRAIDS AND UNIONS OF TRIANGULAR BELTS

  • REDDY, KOTTE AMARANADHA;BASHA, S. SHARIEF
    • Journal of applied mathematics & informatics
    • /
    • v.40 no.1_2
    • /
    • pp.117-132
    • /
    • 2022
  • Reverse edge magic(REM) labeling of the graph G = (V, E) is a bijection of vertices and edges to a set of numbers from the set, defined by λ : V ∪ E → {1, 2, 3, …, |V| + |E|} with the property that for every xy ∈ E, constant k is the weight of equals to a xy, that is λ(xy) - [λ(x) + λ(x)] = k for some integer k. We given the construction of REM labeling for the Cartesian Product, Unions of Braids and Unions of Triangular Belts. The Kotzig array used in this paper is the 3 × (2r + 1) kotzig array. we test the konow results about REM labelling that are related to the new results we found.

A NEW VERTEX-COLORING EDGE-WEIGHTING OF COMPLETE GRAPHS

  • Farahani, Mohammad Reza
    • Journal of applied mathematics & informatics
    • /
    • v.32 no.1_2
    • /
    • pp.1-6
    • /
    • 2014
  • Let G = (V ; E) be a simple undirected graph without loops and multiple edges, the vertex and edge sets of it are represented by V = V (G) and E = E(G), respectively. A weighting w of the edges of a graph G induces a coloring of the vertices of G where the color of vertex v, denoted $S_v:={\Sigma}_{e{\ni}v}\;w(e)$. A k-edge-weighting of a graph G is an assignment of an integer weight, w(e) ${\in}${1,2,...,k} to each edge e, such that two vertex-color $S_v$, $S_u$ be distinct for every edge uv. In this paper we determine an exact 3-edge-weighting of complete graphs $k_{3q+1}\;{\forall}_q\;{\in}\;{\mathbb{N}}$. Several open questions are also included.

Solving L(2,1)-labeling Problem of Graphs using Genetic Algorithms (유전자 알고리즘을 이용한 그래프에서 L(2,1)-labeling 문제 연구)

  • Han, Keun-Hee;Kim, Chan-Soo
    • The KIPS Transactions:PartB
    • /
    • v.15B no.2
    • /
    • pp.131-136
    • /
    • 2008
  • L(2,1)-labeling of a graph G is a function f: V(G) $\rightarrow$ {0, 1, 2, ...} such that $|f(u)\;-\;f(\upsilon)|\;{\geq}\;2$ when d(u, v) = 1 and $|f(u)\;-\;f(\upsilon)|\;{\geq}\;1$ when d(u, $\upsilon$) = 2. L(2,1)-labeling number of G, denoted by ${\lambda}(G)$, is the smallest number m such that G has an L(2,1)-labeling with no label greater than m. Since this problem has been proved to be NP-complete, in this article, we develop genetic algorithms for L(2,1)-labeling problem and show that the suggested genetic algorithm peforms very efficiently by applying the algorithms to the class of graphs with known optimum values.