• Journal of KIISE:Computer Systems and Theory
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• v.32 no.8
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• pp.426-431
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• 2005

A many-to-many k-disjoint path cover (k-DPC) of a graph G is a set of k disjoint paths joining k distinct source-sink pairs in which each vertex of G is covered by a path. In this paper, we investigate many-to-many 2-DPC in a double loop network G(mn;1,m), and show that every nonbipartite G(mn;1,m), $m{\geq}3$, has 2-DPC joining any two source-sink pairs of vertices and that every bipartite G(mn;1,m) has 2-DPC joining any two source-sink pairs of black-white vertices and joining any Pairs of black-black and white-white vertices. G(mn;l,m) is bipartite if and only if n is odd and n is even.

• The Journal of Natural Sciences
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• v.12 no.1
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• pp.1-9
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• 2002

Let G be a connected graph on n vertices. The pebbling number of graph G, f(G), is the least m such that, however m pebbles are placed on the vertices of G, we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles off one vertex and placing one on an adjacent vertex. In this paper, we compute the pebbling number of the Petersen Graph. We also show that the pebbling number of the categorical Product G.H is (m+n)h where G is the complete bipartite graph $K_{m,n}$ and H is the complete graph with $h(\geq4)$ vertices.

• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.161-169
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• 2009

In this paper, we introduce the generalized ideal-based zero-divisor graph structure of near-ring N, denoted by $\widehat{{\Gamma}_I(N)}$. It is shown that if I is a completely reflexive ideal of N, then every two vertices in $\widehat{{\Gamma}_I(N)}$ are connected by a path of length at most 3, and if $\widehat{{\Gamma}_I(N)}$ contains a cycle, then the core K of $\widehat{{\Gamma}_I(N)}$ is a union of triangles and rectangles. We have shown that if $\widehat{{\Gamma}_I(N)}$ is a bipartite graph for a completely semiprime ideal I of N, then N has two prime ideals whose intersection is I.

• 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.

• Proceedings of the Korean Information Science Society Conference
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• 2006.06a
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• pp.403-405
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• 2006

Boolean 회로는 parallel 알고리즘을 위한 단순하면서도 실제적인 모델이다. Chung & Lee은 Boolean 회로 모델에서 볼록 이분할 그래프를 위한 최대 매칭을 찾는 O($log^2n+logn$ loglogn logb)depth와 $O(bn^3)$ size의 알고리즘을 제시하였다. 본 논문에서는 prefix compulsion 및 ASCEND, odd-even-merge의 방법을 이용하여 이를 개선한 O($log^2n$ logb) depth, O($bn^2$ logn) size의 최대 매칭 알고리즘을 제시한다.

• 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.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.22 no.5
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• pp.1-6
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• 2022

This paper deals with the maximum cardinality matching(MCM) problem. The augmenting path technique is well known in MCM. MCM is obtained by $O({\sqrt{n}}m)$ time complexity augmenting path algorithm for the general graph, and O(m log n) algorithm for the bipartite graph. On the other hand, this paper suggests O(n) linear time algorithm. The proposed algorithm based on the basic principle of as possible as largest selected inter-vertex edges in order to obtain the MCM. This paper simply selects edge {u,𝜐} that the minimum degree vertex u and minimum degree vertex 𝜐 in N_G(u) 𝜈(G)=k times iteration. For various general and bipartite graphs experimental data, this algorithm can be get the 𝜈(G) exactly.