• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.215-224
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• 2006

We call the bipartite graph G is normal provided the reduced adjacency matrix A of G is normal. In this paper we give graph representations of normal matrices. In addition we shall have the characterization of signed bipartite normal graphs.

• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.787-790
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• 1998

In this paper we consider strongly polynomial variations of the auction algorithm for the single origin/all destinations shortest path problem. These variations are based on the idea of graph reduction, that is, deleting unnecessary arcs of the graph by using certain bounds naturally obtained in the course of the algorithm. We study the structure of the reduced graph and we exploit this structure to obtain algorithm with O(n min{m, nlogn}) and O(n$^{2}$) running time.

• Proceedings of the Korea Information Processing Society Conference
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• 2017.04a
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• pp.816-819
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• 2017

Current graph mining algorithms suffers from performance issues when querying patterns are in increasingly massive network graphs. However, from our observation most data graphs inherently contains recurring semantic subgraphs/substructures. Most graph mining algorithms treat them as independent subgraphs and perform computations on them redundantly, which result in performance degradation when processing massive graphs. In this paper, we propose an algorithm which exploits these inherent recurring subgraphs/substructures to reduce graph sizes so that redundant computations performed by the traditional graph mining algorithms are reduced. Experimental results show that our graph compression approach achieve up to 69% reduction in graph sizes over the real datasets. Moreover, required time to construct the compressed graphs is also reasonably reduced.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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• pp.205-225
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• 2022

In this paper, we derive analytical closed results for the first (a, b)-KA index, the Sombor index, the modified Sombor index, the first reduced (a, b)-KA index, the reduced Sombor index, the reduced modified Sombor index, the second reduced (a, b)-KA index and the mean Sombor index mSO_α for the OTIS biswapped networks by considering basis graphs as path, wheel graph, complete bipartite graph and r-regular graphs. Network theory plays a significant role in electronic and electrical engineering, such as signal processing, networking, communication theory, and so on. A topological index (TI) is a real number associated with graph networks that correlates chemical networks with a variety of physical and chemical properties as well as chemical reactivity. The Optical Transpose Interconnection System (OTIS) network has recently received increased interest due to its potential uses in parallel and distributed systems.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.601-631
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• 2010

In [6] and [7], we introduced graph von Neumann algebras which are the (groupoid) crossed product algebras of von Neumann algebras and graph groupoids via groupoid actions. We showed that such crossed product algebras have the graph-depending amalgamated reduced free probabilistic properties. In this paper, we will consider a scalar-valued $W^*$-probability on a given graph von Neumann algebra. We show that a diagonal graph $W^*$-probability space (as a scalar-valued $W^*$-probability space) and a graph W¤-probability space (as an amalgamated $W^*$-probability space) are compatible. By this compatibility, we can find the relation between amalgamated free distributions and scalar-valued free distributions on a graph von Neumann algebra. Under this compatibility, we observe the scalar-valued freeness on a graph von Neumann algebra.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.13 no.1
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• pp.63-73
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• 1988

In this paper, an algorithm is proposed to evaluate the source-to-terminal reliability, the probability that a source node can communicate with a terminal node, in a probabilistic derected graph. By using Satyanaratana's factoring $theorem^{(7)}$, the original graph can be partitioned into two reduced graphs obtained by contracting and deleting the edge connected to the source node in the probabilistic directed graph. The edge removal proposed in this paper and the general series-parallel reduction can then be applied to the reduced graph. This edge reduction can be applied recursively to the reduced graphs until a source node can be connected to a terminal node by one edge. A computer program which can be applied to evaluating the source-to-terminal reliability in a complex and large network has also been developed.

• Journal of Korea Multimedia Society
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• v.22 no.2
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• pp.225-230
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• 2019

There are several methods which efficiencies of database are uprise. One of the well-known methods is that segments of database satisfying a query was rapidly accessed and processed. So if it is possible to search completely parallel multiple database segment types which satisfy a query, the response time of the query will be reduced. The matter of obtaining CPS(Completely Parallel Searchable) distribution without redundancy can be viewed as graph theoretic problem, and the operation of ring sum on the graph is used for CPS. In this paper, the parallel algorithm is proposed.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.847-865
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• 2017

For a finite or an infinite set X, let $2^X$ be the power set of X. A class of simple graph, called strong Boolean graph, is defined on the vertex set $2^X{\setminus}\{X,{\emptyset}\}$, with M adjacent to N if $M{\cap}N={\emptyset}$. In this paper, we characterize the annihilating-ideal graphs $\mathbb{AG}(R)$ that are blow-ups of strong Boolean graphs, complemented graphs and preatomic graphs respectively. In particular, for a commutative ring R such that AG(R) has a maximum clique S with $3{\leq}{\mid}V(S){\mid}{\leq}{\infty}$, we prove that $\mathbb{AG}(R)$ is a blow-up of a strong Boolean graph if and only if it is a complemented graph, if and only if R is a reduced ring. If assume further that R is decomposable, then we prove that $\mathbb{AG}(R)$ is a blow-up of a strong Boolean graph if and only if it is a blow-up of a pre-atomic graph. We also study the clique number and chromatic number of the graph $\mathbb{AG}(R)$.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.749-762
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• 2017

The surface singular braid monoid corresponds to marked graph diagrams of knotted surfaces in braid form. In a quest to resolve linearity problem for this monoid, we will show that if it is defined on at least two or at least three strands, then its two or respectively three dimensional representations are not faithful. We will also derive new presentations for the surface singular braid monoid, one with reduced the number of defining relations, and the other with reduced the number of its singular generators. We include surface singular braid formulations of all knotted surfaces in Yoshikawa's table.

• The Transactions of the Korea Information Processing Society
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• v.7 no.8
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• pp.2536-2542
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• 2000

The dominator tree presents the dominance frontier from directed graph to the tree. we present the effective algorithm for constructing the dominator tree from arbitrarY directed graph. The reducible flow graph was reduced to dominator tree after dominator calculation. And the irreducible flow graph was constructed to dominator-join graph using join-edge information of information table. For reducing the dominator tree from dominator-join graph, we present the effective sequency reducible algorithm and delay reducible algorithm.