• Korean Journal of Mathematics
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• v.7 no.1
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• pp.53-60
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• 1999

We find bounds of eigenvalues of bipartite tournament matrices. We see when bipartite matrices exist and how players and teams of the matrices are evenly ranked. Also, we show that a bipartite tournament matrix can be both regular and normal when and only when it has the same team size.

• Kyungpook Mathematical Journal
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• v.19 no.1
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• pp.127-134
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• 1979

A (0,1) matrix is acyclic if it does not have a permutation matrix of order 2 as a submatrix. A bipartite tournament is acyclic if and only if its adjacency matrix is acyclic. The concepts of (maximal) order of cyclicity of a matrix and a bipartite tournament are introduced and studied.

• 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.

• Journal of Digital Contents Society
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• v.19 no.1
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• pp.149-155
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• 2018

In this paper we propose an algorithm for generating role-performer bipartite matrix for analyzing BPM-based human resource affiliations. Firstly, the proposed algorithm conducts the extraction of role-performer affiliation relationships from ICN(Infromation Contorl Net) based business process models. Then, the role-performer bipartite matrix is constructed in the final step of the algorithm. Conclusively, the bipartite matrix generated through the proposed algorithm ought to be used as the fundamental data structure for discovering the role-performer affiliation networking knowledge, and by using a variety of social network analysis techniques it enables us to acquire valuable analysis results about BPM-based human resource affiliations.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.183-190
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• 2001

In this paper, we look at the spectral bounds of a bipartite tournament matrix M with arbitrary team size. Also we find the condition for the variance of the Perron vector of M to vanish.

• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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• pp.255-263
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• 2023

In general, the rigidity problem of braced rectangular frameworks is determined by the connectivity of the bipartite graph induced by given rectangular framework. In this paper, we study how to solve the rigidity problem of the braced rectangular framework using the Laplacian matrix of the matrix induced by a braced rectangular framework.

• Journal of applied mathematics & informatics
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• v.42 no.5
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• pp.1121-1135
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• 2024

In this paper, we introduced a new distance-based index called the minimum degree Wiener index, which is the sum of distances between all unordered pairs of vertices with the minimum degree. Additionally, a matrix related to this index was introduced, and it was discovered that the sum of entries in each row was the same for some classes of graphs, contrary to many graph-related matrices. In particular, we determined the minimum degree Wiener index of the bipartite Kneser graph, bipartite Kneser type-k graphs, Johnson graph and the set inclusion graphs. The terminal Wiener index of a graph G is the sum of distances between all unordered pairs of pendant vertices of G. Also, we determined Wiener index, hyper Wiener index and corresponding polynomials of the bipartite Kneser type-k graphs for k = 2, 3.

• Journal of Internet Computing and Services
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• v.14 no.2
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• pp.25-34
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• 2013

In this paper, we propose an activity-performer bipartite matrix generation algorithm for analyzing workflow-supported human-resource affiliations in a workflow model. The workflow-supported human-resource means that all performers of the organization managed by a workflow management system have to be affiliated with a certain set of activities in enacting the corresponding workflow model. We define an activity-performer affiliation network model that is a special type of social networks representing affiliation relationships between a group of performers and a group of activities in workflow models. The algorithm proposed in this paper generates a bipartite matrix from the activity-performer affiliation network model(APANM). Eventually, the generated activity-performer bipartite matrix can be used to analyze social network properties such as, centrality, density, and correlation, and to enable the organization to obtain the workflow-supported human-resource affiliations knowledge.

• The KIPS Transactions:PartB
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• v.10B no.3
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• pp.265-272
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• 2003

In this paper, we propose a novel improved algorithm for the rectangular decomposition technique for the purpose of performing data mining from large scaled database in a dynamic environment. The proposed algorithm performs the rectangular decompositions by transforming a binary matrix to bipartite graph and finding bicliques from the transformed bipartite graph. To demonstrate its effectiveness, we compare the proposed one which is based on the newly derived mathematical properties with those of other methods with respect to the classification rate, the number of rules, and complexity analysis.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.871-881
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• 2005

In 1977, Ganter and Teirlinck proved that any $2t\;\times\;2t$ matrix with 2t nonzero elements can be partitioned into four sub-matrices of order t of which at most two contain nonzero elements. In 1978, Kramer and Mesner conjectured that any $mt{\times}nt$ matrix with kt nonzero elements can be partitioned into mn submatrices of order t of which at most k contain nonzero elements. In 1995, Brualdi et al. showed that this conjecture is true if $m = 2,\;k\;\leq\;3\;or\;k\geq\;mn-2$. They also found a counterexample of this conjecture when m = 4, n = 4, k = 6 and t = 2. When t = 2, we show that this conjecture is true if $k{\leq}5$.