• Journal of applied mathematics & informatics
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• v.39 no.1_2
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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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• v.34 no.1_2
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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.

• Proceedings of the KIEE Conference
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• 2000.11b
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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.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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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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• v.32 no.3_4
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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.

• School Mathematics
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• v.7 no.4
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• pp.353-373
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• 2005

The purpose of this paper is to analysis the basic network problem which can be applied to the mathematically gifted students in elementary school. Mainly, we discuss didactic transpositions of the double counting principle, the game of sprouts, Eulerian graph problem, and the minimum connector problem. Here the double counting principle is related to the handshaking lemma; in any graph, the sum of all the vertex-degree is equal to the number of edges. The selection of these subjects are based on the viewpoint; to familiar to graph theory, to raise algorithmic thinking, to apply to the real-world problem. The theoretical background of didactic transpositions of these subjects are based on the Polya's mathematical heuristics and Lakatos's philosophy of mathematics; quasi-empirical, proofs and refutations as a logic of mathematical discovery.

• Journal of Applied and Pure Mathematics
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• v.5 no.5_6
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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.

• Proceedings of the KIEE Conference
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• 1988.07a
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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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• v.55 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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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].