• Journal of applied mathematics & informatics
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• 제39권1_2호
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• pp.155-163
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• 2021

For a connected graph G of order n, a set S of vertices is called a double geodetic set of G if for each pair of vertices x, y in G there exist vertices u, v ∈ S such that x, y ∈ I[u, v]. The double geodetic number dg(G) is the minimum cardinality of a double geodetic set. Any double godetic set of cardinality dg(G) is called a dg-set of G. A connected double geodetic set of G is a double geodetic set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected double geodetic set of G is the connected double geodetic number of G and is denoted by dgc(G). A connected double geodetic set of cardinality dgc(G) is called a dgc-set of G. Connected graphs of order n with connected double geodetic number 2 or n are characterized. For integers n, a and b with 2 ≤ a < b ≤ n, there exists a connected graph G of order n such that dg(G) = a and dgc(G) = b. It is shown that for positive integers r, d and k ≥ 5 with r < d ≤ 2r and k - d - 3 ≥ 0, there exists a connected graph G of radius r, diameter d and connected double geodetic number k.

• Journal of applied mathematics & informatics
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• 제34권1_2호
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• pp.9-17
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• 2016

In this paper, it has been shown that the hairy cycle C_n ⊙ rK₁, n ≡ 3(mod4), the graph obtained by adding pendant edge to each pendant vertex of hairy cycle C_n ⊙ 1K₁, n ≡ 0(mod4), double graph of path P_n and double graph of comb P_n ⊙ 1K₁ are k-graceful.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2000년도 추계학술대회 논문집 학회본부 B
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• pp.389-391
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• 2000

A representation technique of a given track topology is required by many software applications in railway technology such as signalling system simulator. To achieve these, the concept of double vertex graph architecture is proposed. These are composed of pairs of vertices and node between the single vertices. Double vertex graph architecture can be understood as a extension of classical graphs. In developed railway signalling simulation software, it is shown that track topology can be represented by proposed algorithm in a efficient way. Especially it makes sure that these are suitable technique for representing and implementing of switch, routes which can be introduced some mistake in classical graph algorithm.

• 대한수학회지
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• 제34권2호
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• pp.337-344
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• 1997

In this paper, we study the isomorphism problem of Cayley permutation graphs. We obtain a necessary and sufficient condition that two Cayley permutation graphs are isomrphic by a direction-preserving and color-preserving (positive/negative) natural isomorphism. The result says that if a graph G is the Cayley graph for a group $\Gamma$ then the number of direction-preserving and color-preserving positive natural isomorphism classes of Cayley permutation graphs of G is the number of double cosets of $\Gamma^\ell$ in $S_\Gamma$, where $S_\Gamma$ is the group of permutations on the elements of $\Gamma and \Gamma^\ell$ is the group of left translations by the elements of $\Gamma$. We obtain the number of the isomorphism classes by counting the double cosets.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.377-387
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• 2014

Let G be a (p, q) graph. Let f be a map from V (G) to {1, 2, ${\ldots}$, p}. For each edge uv, assign the label ${\mid}f(u)-f(\nu){\mid}$. f is called a difference cordial labeling if f is a one to one map and ${\mid}e_f(0)-e_f(1){\mid}{\leq}1$ where $e_f(1)$ and $e_f(0)$ denote the number of edges labeled with 1 and not labeled with 1 respectively. A graph with admits a difference cordial labeling is called a difference cordial graph. In this paper, we investigate the difference cordial labeling behavior of triangular snake, Quadrilateral snake, double triangular snake, double quadrilateral snake and alternate snakes.

• 대한수학교육학회지:학교수학
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• 제7권4호
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• pp.353-373
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• 2005

최근의 급속한 정보화 사회로의 전환에 편승하여 이산수학에 대한 관심과 이에 따른 연구가 활발해지고 있으며, 제 7차 교육과정에서 이산수학을 선택과목으로 지정할 만큼 그 중요성이 인정되고 있다. 본 연구는 네트워크문제와 관련된 이중계수 문제, 한붓그리기, 그리고 도로망문제를 중심으로, 초등 수학영재학생을 위한 학습프로그램을 구성하는 문제와 관련된 교수학적 변환에 대하여 논의하였다.

• Journal of Applied and Pure Mathematics
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• 제5권5_6호
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• pp.363-373
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• 2023

In this paper we investigate the 4-total mean cordial labeling behavior of arrow graphs, shell-Butterfly graph and graphs obtained by joining two copies of shell graphs by a path.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1988년도 전기.전자공학 학술대회 논문집
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• pp.687-690
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• 1988

Algorithms that represent given pattern in the form of an ARG (Attributed relational graph) using not only structural relations but also symbolic or numerical attributes, and then recognize that pattern by graph matching process are presented in this paper. Based on definitions of pattern deformational models, algorithms that can find GPECI(Graph preserved error correcting isomorphism). SGECI(subgraph ECI) and DSECI(Double subgraph ECI) are proposed and comparisons among these algorithms are described. To be useful in performig practical tasks, efficient schemes for extraction of ARG representation fron raw image are needed. In this study, given patterns are restricted within objects having distinct skeleton, and then the information which is necessary for recognition and analysis is successfully extracted.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.279-287
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• 2015

A subset S of V (G), where G is a graph without isolated vertices, is a double dominating set of G if for each $x{{\in}}V(G)$, ${\mid}N_G[x]{\cap}S{\mid}{\geq}2$. This paper, shows that any positive integers a, b and n with $2{\leq}a<b$, $b{\geq}2a$ and $n{\geq}b+2a-2$, can be realized as domination number, double domination number and order, respectively. It also characterize the double dominating sets in the Cartesian and tensor products of two graphs and determine sharp bounds for the double domination numbers of these graphs. In particular, it show that if G and H are any connected non-trivial graphs of orders n and m respectively, then ${\gamma}_{{\times}2}(G{\square}H){\leq}min\{m{\gamma}_2(G),n{\gamma}_2(H)\}$, where ${\gamma}_2$, is the 2-domination parameter.

• 대한수학회보
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• 제59권1호
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• pp.167-177
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• 2022

A vertex v of a graph G = (V, E) is said to ve-dominate every edge incident to v, as well as every edge adjacent to these incident edges. A set S ⊆ V is called a double vertex-edge dominating set if every edge of E is ve-dominated by at least two vertices of S. The minimum cardinality of a double vertex-edge dominating set of G is the double vertex-edge domination number γ_dve(G). In this paper, we provide an upper bound on the double vertex-edge domination number of trees in terms of the order n, the number of leaves and support vertices, and we characterize the trees attaining the upper bound. Finally, we design a polynomial time algorithm for computing the value of γ_dve(T) for any trees. This gives an answer of an open problem posed in [4].