• Title/Summary/Keyword: Graph Labeling

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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.

The Research of the 2-Edge Labeling Methods on Binomial Trees (이항트리에서 2-에지번호매김 방법에 대한 연구)

  • Kim, Yong Seok
    • KIPS Transactions on Computer and Communication Systems
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    • v.4 no.2
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    • pp.37-40
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    • 2015
  • In this paper, we present linear, varied and mixed edge labeling methods using 2-edge labeling on binomial trees. As a result of this paper, we can design the variable topologies to enable optimal broadcasting with binomial tree as spanning tree, if we use these edge labels as the jump sequence of a sort of interconnection networks, circulant graph, with maximum connectivity and high reliability.

THE λ-NUMBER OF THE CARTESIAN PRODUCT OF A COMPLETE GRAPH AND A CYCLE

  • Kim, Byeong Moon;Song, Byung Chul;Rho, Yoomi
    • Korean Journal of Mathematics
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    • v.21 no.2
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    • pp.151-159
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    • 2013
  • An $L(j,k)$-labeling of a graph G is a vertex labeling such that the difference of the labels of any adjacent vertices is at least $j$ and that of any vertices of distance two is at least $k$ for given $j$ and $k$. The minimum span of all L(2, 1)-labelings of G is called the ${\lambda}$-number of G and is denoted by ${\lambda}(G)$. In this paper, we find a lower bound of the ${\lambda}$-number of the Cartesian product $K_m{\Box}C_n$ of the complete graph $K_m$ of order $m$ and the cycle $C_n$ of order $n$. In fact, we show that when $n{\geq}3$, ${\lambda}(K_4{\Box}C_n){\geq}7$ and the equality holds if and only if n is a multiple of 8. Moreover when $m{\geq}5$, ${\lambda}(K_m{\Box}C_n){\geq}2m-1$ and the equality holds if and only if $n$ is even.

The S-Edge Numbering on Binomial trees (이항트리에서 S-에지번호 매김)

  • Kim Yong-Seok
    • Proceedings of the IEEK Conference
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    • 2004.06a
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    • pp.167-170
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    • 2004
  • We present a novel graph labeling problem called S-edge labeling. The constraint in this labeling is placed on the allowable edge label which is the difference between the labels of endvertices of an edge. Each edge label should be ${ a_n / a_n = 4 a_{n-l}+l,\;a_{n-1}=0}$. We show that every binomial tree is possible S-edge labeling by giving labeling schems to them. The labelings on the binomial trees are applied to their embedings into interconnection networks.

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The Fibonacci Edge Labeling on Fibonacci Trees

  • Kim, yong-Seok
    • Proceedings of the IEEK Conference
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    • 2000.07b
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    • pp.731-734
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    • 2000
  • We present a novel graph labeling problem called Fibonacci edge labeling. The constraint in this labeling is placed on the allowable edge label which is the difference between the labels of endvertices of an edge. Each edge label should be (3m+2)-th Fibonacci numbers. We show that every Fibonacci tree can be labeled Fibonacci edge labeling. The labelings on the Fibonacci trees are applied to their embeddings into Fibonacci Circulants.

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Automated Segmentation of the Lateral Ventricle Based on Graph Cuts Algorithm and Morphological Operations

  • Park, Seongbeom;Yoon, Uicheul
    • Journal of Biomedical Engineering Research
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    • v.38 no.2
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    • pp.82-88
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    • 2017
  • Enlargement of the lateral ventricles have been identified as a surrogate marker of neurological disorders. Quantitative measure of the lateral ventricle from MRI would enable earlier and more accurate clinical diagnosis in monitoring disease progression. Even though it requires an automated or semi-automated segmentation method for objective quantification, it is difficult to define lateral ventricles due to insufficient contrast and brightness of structural imaging. In this study, we proposed a fully automated lateral ventricle segmentation method based on a graph cuts algorithm combined with atlas-based segmentation and connected component labeling. Initially, initial seeds for graph cuts were defined by atlas-based segmentation (ATS). They were adjusted by partial volume images in order to provide accurate a priori information on graph cuts. A graph cuts algorithm is to finds a global minimum of energy with minimum cut/maximum flow algorithm function on graph. In addition, connected component labeling used to remove false ventricle regions. The proposed method was validated with the well-known tools using the dice similarity index, recall and precision values. The proposed method was significantly higher dice similarity index ($0.860{\pm}0.036$, p < 0.001) and recall ($0.833{\pm}0.037$, p < 0.001) compared with other tools. Therefore, the proposed method yielded a robust and reliable segmentation result.

ON 4-TOTAL MEAN CORDIAL GRAPHS

  • PONRAJ, R.;SUBBULAKSHMI, S.;SOMASUNDARAM, S.
    • Journal of applied mathematics & informatics
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    • v.39 no.3_4
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    • pp.497-506
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    • 2021
  • Let G be a graph. Let f : V (G) → {0, 1, …, k - 1} be a function where k ∈ ℕ and k > 1. For each edge uv, assign the label $f(uv)={\lceil}{\frac{f(u)+f(v)}{2}}{\rceil}$. f is called k-total mean cordial labeling of G if ${\mid}t_{mf}(i)-t_{mf}(j){\mid}{\leq}1$, for all i, j ∈ {0, 1, …, k - 1}, where tmf (x) denotes the total number of vertices and edges labelled with x, x ∈ {0, 1, …, k-1}. A graph with admit a k-total mean cordial labeling is called k-total mean cordial graph.

Efficient Authorization Conflict Detection Using Prime Number Graph Labeling in RDF Access Control (RDF 접근 제어에서 소수 그래프 레이블링을 사용한 효율적 권한 충돌 발견)

  • Kim, Jae-Hoon;Park, Seog
    • Journal of KIISE:Databases
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    • v.35 no.2
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    • pp.112-124
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    • 2008
  • RDF and OWL are the primary base technologies for implementing Semantic Web. Recently, many researches related with them, or applying them into the other application domains, have been introduced. However, relatively little work has been done for securing the RDF and OWL data. In this article, we briefly introduce an RDF triple based model for specifying RDF access authorization related with RDF security. Next, to efficiently find the authorization conflict by RDF inference, we introduce a method using prime number graph labeling in detail. The problem of authorization conflict by RDF inference is that although the lower concept is permitted to be accessed, it can be inaccessible due to the disapproval for the upper concept. Because by the RDF inference, the lower concept can be interpreted into the upper concept. Some experimental results show that the proposed method using the prime number graph labeling has better performance than the existing simple method for the detection of the authorization conflict.

H-V -SUPER MAGIC DECOMPOSITION OF COMPLETE BIPARTITE GRAPHS

  • KUMAR, SOLOMON STALIN;MARIMUTHU, GURUSAMY THEVAR
    • Communications of the Korean Mathematical Society
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    • v.30 no.3
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    • pp.313-325
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    • 2015
  • An H-magic labeling in a H-decomposable graph G is a bijection $f:V(G){\cup}E(G){\rightarrow}\{1,2,{\cdots},p+q\}$ such that for every copy H in the decomposition, $\sum{_{{\upsilon}{\in}V(H)}}\;f(v)+\sum{_{e{\in}E(H)}}\;f(e)$ is constant. f is said to be H-V -super magic if f(V(G))={1,2,...,p}. In this paper, we prove that complete bipartite graphs $K_{n,n}$ are H-V -super magic decomposable where $$H{\sim_=}K_{1,n}$$ with $n{\geq}1$.

DISTINGUISHING NUMBER AND DISTINGUISHING INDEX OF STRONG PRODUCT OF TWO GRAPHS

  • Alikhani, Saeid;Soltani, Samaneh
    • Honam Mathematical Journal
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    • v.42 no.4
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    • pp.645-651
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    • 2020
  • The distinguishing number (index) D(G) (D'(G)) of a graph G is the least integer d such that G has an vertex labeling (edge labeling) with d labels that is preserved only by a trivial automorphism. The strong product G ☒ H of two graphs G and H is the graph with vertex set V (G) × V (H) and edge set {{(x1, x2),(y1, y2)}|xiyi ∈ E(Gi) or xi = yi for each 1 ≤ i ≤ 2.}. In this paper we study the distinguishing number and the distinguishing index of strong product of two graphs. We prove that for every k ≥ 2, the k-th strong power of a connected S-thin graph G has distinguishing index equal two.