• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.513-519
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• 2012

For a spanning tree T of a connected graph ${\Gamma}$ and for a labelling ${\phi}$: E(T) ${\rightarrow}$ {+,-},${\phi}$ is called an alternating sign on a spanning tree T of a graph ${\Gamma}$ if for any cotree edge $e{\in}E({\Gamma})-E(T)$, the unique path in T joining both end vertices of e has alternating signs. In the present article, we prove that any graph has a spanning tree T and an alternating sign on T.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.12
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• pp.5401-5421
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• 2016

Both low-density parity-check (LDPC) codes and the multiple access technique of spatially coupling data transmission (SCDT) can be expressed in bipartite graphs. To improve the performance of iterative demodulation and decoding for SCDT, a novel joint sparse graph (JSG) with SCDT and LDPC codes is constructed. Based on the JSG, an approach for iterative joint demodulation and decoding by belief propagation (BP) is presented as an exploration of the flooding schedule, and based on BP, density evolution equations are derived to analyze the performance of the iterative receiver. To accelerate the convergence speed and reduce the complexity of joint demodulation and decoding, a novel serial schedule is proposed. Numerical results show that the joint demodulation and decoding for SCDT based on JSG can significantly improve the system's performance, while roughly half of the iterations can be saved by using the proposed serial schedule.

• 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 Information Processing Systems
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• v.13 no.5
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• pp.1243-1258
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• 2017

A new medical materials scheduling system and its modeling method for the complex rescue are presented. Different from other similar system, first both the BeiDou Satellite Communication System (BSCS) and the Special Fiber-optic Communication Network (SFCN) are used to collect the rescue requirements and the location information of disaster areas. Then all these messages will be displayed in a special medical software terminal. After that the bipartite graph models are utilized to compute the optimal scheduling of medical materials. Finally, all these results will be transmitted back by the BSCS and the SFCN again to implement a fast guidance of medical rescue. The sole drug scheduling issue, the multiple drugs scheduling issue, and the backup-scheme selection issue are all utilized: the Kuhn-Munkres algorithm is used to realize the optimal matching of sole drug scheduling issue, the spectral clustering-based method is employed to calculate the optimal distribution of multiple drugs scheduling issue, and the similarity metric of neighboring matrix is utilized to realize the estimation of backup-scheme selection issue of medical materials. Many simulation analysis experiments and applications have proved the correctness of proposed technique and system.

• Bulletin of the Korean Mathematical Society
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• v.33 no.2
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• pp.311-318
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• 1996

For positive integral vectors $R = (r_1, \cdots, r_m)$ and $S = (s_1, \cdots, s_n)$, we consider the class $U(R,S)$ of all $m \times n$ matrices of 0's and 1's with the row sum vector R and the column sum vector S.

• Honam Mathematical Journal
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• v.41 no.4
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• pp.863-870
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• 2019

In this paper, we obtain the enumeration results on the number of linear extensions of diamond posets. We find the recurrence relations and exponential generating functions for the number of linear extensions of diamond posets. We also get some results for the volume of graph polytope associated with bipartite graphs which are underlying graphs of diamond posets.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.119-126
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• 1996

In this paper we study the asymptotic behavior of the edge independence number of a random (n,n)-tree. The tools we use include the matrix-tree theorem, the probabilistic method and Hall's theorem. We begin with some definitions. An (n,n)_tree T is a connected, acyclic, bipartite graph with n light and n dark vertices (see [Pa92]). A subset M of edges of a graph is called independent(or matching) if no two edges of M are adfacent. A subset S of vertices of a graph is called independent if no two vertices of S are adjacent. The edge independence number of a graph T is the number $\beta_1(T)$ of edges in any largest independent subset of edges of T. Let $\Gamma(n,n)$ denote the set of all (n,n)-tree with n light vertices labeled 1, $\ldots$, n and n dark vertices labeled 1, $\ldots$, n. We give $\Gamma(n,n)$ the uniform probability distribution. Our aim in this paper is to find bounds on $\beta_1$(T) for a random (n,n)-tree T is $\Gamma(n,n)$.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.301-307
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• 2017

In this paper, we solve the following four graph equations $L^k(G)=H{\oplus}J$; $M(G)=H{\oplus}J$; ${\bar{L^k(G)}}=H{\oplus}J$ and ${\bar{M(G)}}=H{\oplus}J$, where J is $nK_2$ for $n{\geq}1$. Here, the equality symbol = means the isomorphism between the corresponding graphs. In particular, we shall obtain all pairs of graphs (G, H), which satisfy the above mentioned equations, upto isomorphism.

• Proceedings of the Korea Information Processing Society Conference
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• 2004.05a
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• pp.777-780
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• 2004

본 논문은 여러 개체의 생물체 궤적을 효과적으로 추적하기 위해 Hungarian Algorithm을 이용한다. 생물체 궤적 정보와 생물체의 좌표 정보로 Weighted bipartite graph를 구성한다. weight는 궤적 정보와 좌표 정보의 거리, 속도, 각도를 비교하여 계산한다. 구성된 graph를 Hungarian Algorithm로 계산하여 가장 효율적인 matching이 이루어지도록 한다. 실제 생물체를 관찰하고 얻어진 데이터를 이용하여 실험을 하고, 제안한 방법의 효율성을 검증한다.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.685-695
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• 2022

The minimum number of complete bipartite subgraphs needed to partition the edges of a graph G is denoted by b(G). A known lower bound on b(G) states that b(G) ≥ max{p(G), q(G)}, where p(G) and q(G) are the numbers of positive and negative eigenvalues of the adjacency matrix of G, respectively. When equality is attained, G is said to be eigensharp and when b(G) = max{p(G), q(G)} + 1, G is called an almost eigensharp graph. In this paper, we investigate the eigensharpness and almost eigensharpness of lexicographic products of some graphs.