• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.4
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• pp.233-241
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• 2014

This paper suggests a fast minimum spanning tree algorithm which simplify the original graph to 2-edge connected graph, and using the cycling property. Borůvka algorithm firstly gets the partial spanning tree using cycle property for one-edge connected graph that selects the only one minimum weighted edge (e) per vertex (v). Additionally, that selects minimum weighted edge between partial spanning trees using cut property. Kruskal algorithm uses cut property for ascending ordered of all edges. Reverse-delete algorithm uses cycle property for descending ordered of all edges. Borůvka and Kruskal algorithms always perform |e| times for all edges. The proposed algorithm obtains 2-edge connected graph that selects 2 minimum weighted edges for each vertex firstly. Secondly, we use cycle property for 2-edges connected graph, and stop the algorithm until |e|=|v|-1 For actual 10 benchmark data, The proposed algorithm can be get the minimum spanning trees. Also, this algorithm reduces 60% of the trial number than Borůvka, Kruskal and Reverse-delete algorithms.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.22 no.11
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• pp.1538-1543
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• 2018

For n pairs of points (a,b) on a circle, the line segment to connect two points is called a chord. These chords define a new graph G. Each chord corresponds to a vertex of G, and if two chords intersect, the two vertices corresponding to them are connected by an edge. This makes a graph, called by a circle graph. In this paper, we deal with the problem to find the connected components of a circle graph. The connected component of a graph G is a maximal subgraph H such that any two vertices in H can be connected by a path. When the adjacent matrix of G is given, the problem to find them can be solved by either the depth-first search or the breadth-first search. But when only the information for the chords is given as an input, it takes ${\Omega}(n^2)$ time to obtain the adjacent matrix. In this paper, we do not make the adjacent matrix and develop an $O(n{\log}^2n)$ algorithm for the problem.

• Proceedings of the Korea Information Processing Society Conference
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• 2018.10a
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• pp.984-987
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• 2018

In an Internet of Thing (IoT) environment, entities with different attributes and capacities are going to be connected in a highly connected fashion. Specifically, not only the mechanical and electronic devices but also other entities such as people, locations and applications are connected to each other. Understanding and managing these connections play an important role for businesses, which identify opportunities for new IoT services. Traditional approach for storing and querying IoT data is used of a relational database management system (RDMS) such as MySQL or MSSQL. However, using RDMS is not flexible and sufficient for handling heterogeneous IoT data because these data have deeply complex relationships which require nested queries and complex joins on multiple tables. In this paper, we propose a graph model for constructing a graph database of heterogeneous IoT data. Graph databases are purposely-built to store highly connected data with nodes representing entities and edges representing the relationships between these entities. Our model fuses social graph, spatial graph, and things graph, and incorporates the relationships among them. We then present a case study which applies our model for representing data from a Smart Campus using Neo4J platform. Through the results of querying to answer real questions in Smart Campus management, we show the viability of our model.

• 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 Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.18 no.1
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• pp.19-29
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• 2020

This paper gives two graph-based algorithms for radioactive decay computation. The first algorithm identifies the connected components of the graph induced from the given radioactive decay dynamics to reduce the size of the problem. The solutions are derived over the precalculated connected components, respectively and independently. The second algorithm utilizes acyclic structure of radioactive decay dynamics. The algorithm evaluates the reachable vertices of the induced system graph from the initially activated vertices and finds the minimal set of starting vertices populating the entire reachable vertices. Then, the decay calculations are performed over the reachable vertices from the identified minimal starting vertices, respectively, with the partitioned initial value over the reachable vertices. Formal arguments are given to show that the proposed graph inspired divide and conquer calculation methods perform the intended radioactive decay calculation. Empirical efforts comparing the proposed radioactive decay calculation algorithms are presented.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.595-613
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• 2022

Let R be a commutative ring with identity and let I be a proper ideal of R. In this paper, we study the ideal based extended zero-divisor graph 𝚪'_I (R) and prove that 𝚪'_I (R) is connected with diameter at most two and if 𝚪'_I (R) contains a cycle, then girth is at most four girth at most four. Furthermore, we study affinity the connection between the ideal based extended zero-divisor graph 𝚪'_I (R) and the ideal-based zero-divisor graph 𝚪_I (R) associated with the ideal I of R. Among the other things, for a radical ideal of a ring R, we show that the ideal-based extended zero-divisor graph 𝚪'_I (R) is identical to the ideal-based zero-divisor graph 𝚪_I (R) if and only if R has exactly two minimal prime-ideals which contain I.

• 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.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.295-299
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• 1999

Every quasi-random graph G(n) on n vertices consists of a giant component plus o(n) vertices, and every quasi-random graph G(n) with minimum degree (1+o(1))\ulcorner is connected.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.57-61
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• 2002

Let G be a connected graph. A pebbling move on a graph G is the movement of taking two pebbles off from a vertex and placing one of them onto an adjacent vertex. The pebbling number f(G) of a connected graph G is the least n such that any distribution of n pebbles on the vertices of G allows one pebble to be moved to any specified, but arbitrary vertex by a sequence of pebbling moves. In this paper, the pebbling numbers of the compositions of two graphs are computed.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.637-646
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• 2011

Cho and Kim [4] and Kim [6] introduced the concept of the competition index of a digraph. Cho and Kim [4] and Akelbek and Kirkland [1] also studied the upper bound of competition indices of primitive digraphs. In this paper, we study the upper bound of competition indices of strongly connected digraphs. We also study the relation between competition index and ordinary index for a symmetric strongly connected digraph.