• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2004년도 하계종합학술대회 논문집(1)
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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.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2000년도 ITC-CSCC -2
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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.

• Journal of Electrical Engineering and Technology
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• 제6권4호
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• pp.580-584
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• 2011

Corner positioning templates are proposed in order to detect the accurate positions of corners that are extracted using 4-directional edge labeling. Top-down and bottom-up directional labeling are used to label the edge segments with four kinds of labels according to their directions. The points whose labels have changed are then determined as corners. The exact positions of the missing corners due to the disconnected edges are detected through the corner positioning templates that are determined according to the labels of start-points and end-points after the two-pass edge labeling. Experiment results show that the proposed method can detect the exact positions of the real corners.

• 정보처리학회논문지:컴퓨터 및 통신 시스템
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• 제4권2호
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• pp.37-40
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• 2015

본 논문에서는 이항트리의 2-에지번호매김에서 선형적 에지번호매김 방법, 변형된 에지번호매김 방법 그리고 혼합형 에지번호매김 방법들을 제안한다. 이러한 연구결과는 최대 연결도를 갖는 신뢰성이 높은 상호연결망의 일종인 원형군 그래프(circulant graph)의 점프열(jump sequence)로 에지번호들을 사용하면 이항트리를 스패닝 트리로 갖고 최적방송이 가능한 다양한 위상들을 설계할 수 있다.

• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.117-132
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• 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.

• Journal of applied mathematics & informatics
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• 제39권1_2호
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• pp.223-237
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• 2021

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 square of the path, duplication of a vertex by a new edge in path and cycle graphs, duplication of an edge by a new vertex in path and cycle graphs and total graph of cycle and path graphs admit a group S3 cordial remainder labeling.

• Journal of applied mathematics & informatics
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• 제42권2호
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• pp.367-377
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• 2024

Let G = (V, E) be a graph with p-vertices and q-edges and let R^◦ be a finite zero ring of order n. An injective function f : V (G) → {r₁, r₂, _…, r_k}, where r_i ∈ R^◦ is called vertex pair sum k-zero ring labeling, if it is possible to label the vertices x ∈ V with distinct labels from R^◦ such that each edge e = uv is labeled with f(e = uv) = [f(u) + f(v)] (mod n) and the edge labels are distinct. A graph admits such labeling is called vertex pair sum k-zero ring graph. The minimum value of positive integer k for a graph G which admits a vertex pair sum k-zero ring labeling is called the vertex pair sum k-zero ring index denoted by 𝜓_pz(G). In this paper, we defined the vertex pair sum k-zero ring labeling and applied to some graphs.

• 대한수학회보
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• 제45권1호
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• pp.11-21
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• 2008

A graph G = (V, E) is called super edge-magic if there exists a one-to-one map $\lambda$ from V $\cup$ E onto {1,2,3,...,|V|+|E|} such that $\lambda$(V)={1,2,...,|V|} and $\lambda(x)+\lambda(xy)+\lambda(y)$ is constant for every edge xy. In this paper, we investigate whether some families of graphs are super edge-magic or not.

• 한국정보과학회논문지:시스템및이론
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• 제36권6호
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• pp.437-450
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• 2009

본 논문에서는 임의의 피보나치 트리에 에지번호매김을 하여 피보나치 수들의 집합 {$F_k|k\;{\geq}\;2$}, {$F_{2k}|k\;{\geq}\;1$} 그리고 {$F_{3k+2}|k\;{\geq}\;0$}인 세가지 경우의 에지번호 집합을 얻는 7가지의 에지번호매김방법들을 제안한다. 이러한 에지번호들의 집합은 상호연결망의 일종인 원형군의 설계시 점프열로 사용할 수 있으므로 망척도 중 하나인 분지수를 결정한다.

• Korean Journal of Mathematics
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• 제23권4호
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• pp.607-618
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• 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.