• Journal of Korean Institute of Industrial Engineers
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• v.20 no.3
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• pp.3-14
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• 1994

In this study, two reliability computational algorithms which respectively utilize a factoring method are proposed for a system represented by reliability block diagram. First, vertex factoring algorithm is proposed. In this algorithm, a reliability block diagram is considered as a network graph with vertex reliabilities. Second algorithm is mainly concerned with conversion of a reliabilities block diagram into a network graph with edge reliabilities. In this algorithm, the independence of edges is preserved by eliminating replicated edges, and in computing the reliability of a converted network graph, existing edge factoring algorithm is applied. The efficiency of two algorithms are compared for example systems with respect to computing times. The results shows that the second algorithm is shown to be more efficient than the first algorithm.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.201-215
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• 2003

A map is a connected topological graph $\Gamma$ cellularly embedded in a surface. For any connected graph $\Gamma$, by introducing the concertion of semi-arc automorphism group Aut$\_$$\frac{1}{2}$/$\Gamma$ and classifying all embedding of $\Gamma$ undo. the action of this group, the numbers r$\^$O/ ($\Gamma$) and r$\^$N/($\Gamma$) of rooted maps on orientable and non-orientable surfaces with underlying graph $\Gamma$ are found. Many closed formulas without sum ∑ for the number of rooted maps on surfaces (orientable or non-orientable) with given underlying graphs, such as, complete graph K$\_$n/, complete bipartite graph K$\_$m, n/ bouquets B$\_$n/, dipole Dp$\_$n/ and generalized dipole (equation omitted) are refound in this paper.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.2
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• pp.359-370
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• 1997

We consider a facility layout problem with the objective of minimizing total transportation distance, which is the sum of rectilinear distances between facilities weighted by the frequency of trips between the facilities. It is assumed that facilities are required to have rectangular shapes and there is no empty space between the facilities in the layout. In this study, a graph theoretic heuristic is developed for the problem. In the heuristic, planar graphs are constructed to represent adjacencies between the facilities and then the graphs are converted to block layouts on a continual plane using a layout construction module. (Therefore, each graph corresponds to a layout.) An initial layout is obtained by constructing a maximal weighted planar graph and then the layout is improved by changing the planar graph. A simulated annealing algorithm is used to find a planar graph which gives the best layout. To show the performance of the proposed heuristic, computational experiments are done on randomly generated test problems and results are reported.

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.51-61
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• 2022

Let G be a graph. Let f : V (G) → {0, 1, 2, …, k-1} be a map where k ∈ ℕ and k > 1. For each edge uv, assign the label |f(u) - f(v)|. f is called k-total difference cordial labeling of G if |t_df (i) - t_df (j) | ≤ 1, i, j ∈ {0, 1, 2, …, k - 1} where t_df (x) denotes the total number of vertices and the edges labeled with x. A graph with admits a k-total difference cordial labeling is called k-total difference cordial graphs. In this paper we investigate the 4-total difference cordial labeling behaviour of shell butterfly graph, Lilly graph, Shackle graphs etc..

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.123-137
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• 2024

In this paper, Power fuzzy graphs is newly introduced by allotting fuzzy values on power graphs in such a way that the newly added edges, has the edge membership values between a closed interval which depends on vertex membership values and the length of the added edges. Power fuzzy subgraphs and total power fuzzy graphs are newly defined with properties and some special cases. It is observed that every power fuzzy graph is a fuzzy graph but the converse need not be true. Edges that are incident to vertices with the least vertex membership values are retained in the least power fuzzy subgraph. Further, the application of these concepts in real life time has been presented and discussed using power fuzzy graph model.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.341-354
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• 2016

In this paper, the exact formulae for the generalized product degree distance, reciprocal product degree distance and product degree distance of tensor product of a connected graph and the complete multipartite graph with partite sets of sizes m₀, m₁, ⋯ , m_r−1 are obtained.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.531-540
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• 2008

We discuss the decomposition problems on circuit graphs and triangular graphs, and show how they can be applied to obtain results on spanning trees or hamiltonian cycles. We also prove that every circuit graph containing no separating 3-cycles can be extended by adding new edges to a triangular graph containing no separating 3-cycles.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.235-242
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• 1997

We characterize the tight structure of a vertex-accumula-tion-free maximal planar graph with no separating triangles. Together with the result of Halin who gave an equivalent form for such graphs this yields that a tight structure always exists in every 4-connected maximal planar graph with one end.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.851-860
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• 2008

A countable locally finite triangulation is a strong triangulation if a representation of the graph contains no vertex- or edge-accumulation points. In this paper we exhibit the structure of an infinite strong triangulation and prove the existence of connected spanning subgraph with maximum degree 4 in such a graph

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.537-543
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• 2005

A graph is k-cyclable if given k vertices there is a cycle that contains the k vertices. Sallee showed that every finite 3-connected planar graph is 5-cyclable. In this paper Sallee's result is extended to 3-connected infinite locally finite VAP-free plane graphs containing no unbounded faces.