• Title/Summary/Keyword: circulant graph

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The Research of Q-edge Labeling on Binomial Trees related to the Graph Embedding (그래프 임베딩과 관련된 이항 트리에서의 Q-에지 번호매김에 관한 연구)

  • Kim Yong-Seok
    • Journal of the Institute of Electronics Engineers of Korea CI
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    • v.42 no.1
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    • pp.27-34
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    • 2005
  • In this paper, we propose the Q-edge labeling method related to the graph embedding problem in binomial trees. This result is able to design a new reliable interconnection networks with maximum connectivity using Q-edge labels as jump sequence of circulant graph. The circulant graph is a generalization of Harary graph which is a solution of the optimal problem to design a maximum connectivity graph consists of n vertices End e edgies. And this topology has optimal broadcasting because of having binomial trees as spanning tree.

Generalized characteristic polynomials of semi-zigzag product of a graph and circulant graphs

  • Lee, Jae-Un;Kim, Dong-Seok
    • Journal of the Korean Data and Information Science Society
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    • v.19 no.4
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    • pp.1289-1295
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    • 2008
  • We find the generalized characteristic polynomial of graphs G($F_{1},F_{2},{\cdots},F_{v}$) the semi-zigzag product of G and ${\{F_{i}\}^{v}_{i=1}$ obtained from G by replacing vertices by circulant graphs of vertices and joining $F_{i}$'s along the edges of G. These graphs contain discrete tori and are key examples in the study of network model.

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NORMAL EDGE-TRANSITIVE CIRCULANT GRAPHS

  • Sim, Hyo-Seob;Kim, Young-Won
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.2
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    • pp.317-324
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    • 2001
  • A Cayley graph of a finite group G is called normal edge-transitive if its automorphism group has a subgroup which both normalized G and acts transitively on edges. In this paper, we consider Cayley graphs of finite cyclic groups, namely, finite circulant graphs. We characterize the normal edge-transitive circulant graphs and determine the normal edge-transitive circulant graphs of prime power order in terms of lexicographic products.

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A DIFFERENCE SET METHOD FOR CIRCULANT DECOMPOSITIONS OF COMPLETE PARTITE GRAPHS INTO GREGARIOUS 4-CYCLES

  • Kim, Eun-Kyung;Cho, Young-Min;Cho, Jung-Rae
    • East Asian mathematical journal
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    • v.26 no.5
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    • pp.655-670
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    • 2010
  • The complete multipartite graph $K_{n(m)}$ with n $ {\geq}$ 4 partite sets of size m is shown to have a decomposition into 4-cycles in such a way that vertices of each cycle belong to distinct partite sets of $K_{n(m)}$, if 4 divides the number of edges. Such cycles are called gregarious, and were introduced by Billington and Hoffman ([2]) and redefined in [3]. We independently came up with the result of [3] by using a difference set method, and improved the result so that the composition is circulant, in the sense that it is invariant under the cyclic permutation of partite sets. The composition is then used to construct gregarious 4-cycle decompositions when one partite set of the graph has different cardinality than that of others. Some results on joins of decomposable complete multipartite graphs are also presented.

Topological Properties of Recursive Circulants : Disjoint Cycles and Graph Invariants (재귀원형군의 위상 특성 : 서로소인 사이클과 그래프 invariant)

  • Park, Jeong-Heum;Jwa, Gyeong-Ryong
    • Journal of KIISE:Computer Systems and Theory
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    • v.26 no.8
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    • pp.999-1007
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    • 1999
  • 이 논문은 재귀원형군 G(2^m , 2^k )를 그래프 이론적 관점에서 고찰하고 정점이 서로소인 사이클과 그래프 invariant에 관한 위상 특성을 제시한다. 재귀원형군은 1 에서 제안된 다중 컴퓨터의 연결망 구조이다. 재귀원형군 {{{{G(2^m , 2^k )가 길이 사이클을 가질 필요 충분 조건을 구하고, 이 조건하에서 G(2^m , 2^k )는 가능한 최대 개수의 정점이 서로소이고 길이가l`인 사이클을 가짐을 보인다. 그리고 정점 및 에지 채색, 최대 클릭, 독립 집합 및 정점 커버에 대한 그래프 invariant를 분석한다.Abstract In this paper, we investigate recursive circulant G(2^m , 2^k ) from the graph theory point of view and present topological properties of G(2^m , 2^k ) concerned with vertex-disjoint cycles and graph invariants. Recursive circulant is an interconnection structure for multicomputer networks proposed in 1 . A necessary and sufficient condition for recursive circulant {{{{G(2^m , 2^k ) to have a cycle of lengthl` is derived. Under the condition, we show that G(2^m , 2^k ) has the maximum possible number of vertex-disjoint cycles of length l`. We analyze graph invariants on vertex and edge coloring, maximum clique, independent set and vertex cover.

LINEAR AND NON-LINEAR LOOP-TRANSVERSAL CODES IN ERROR-CORRECTION AND GRAPH DOMINATION

  • Dagli, Mehmet;Im, Bokhee;Smith, Jonathan D.H.
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.2
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    • pp.295-309
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    • 2020
  • Loop transversal codes take an alternative approach to the theory of error-correcting codes, placing emphasis on the set of errors that are to be corrected. Hitherto, the loop transversal code method has been restricted to linear codes. The goal of the current paper is to extend the conceptual framework of loop transversal codes to admit nonlinear codes. We present a natural example of this nonlinearity among perfect single-error correcting codes that exhibit efficient domination in a circulant graph, and contrast it with linear codes in a similar context.

Genesis and development of Schur rings, as a bridge of group and algebraic graph theory (Schur환론의 발생과 발전, 군론과 그래프론에서의 역할)

  • Choi Eun-Mi
    • Journal for History of Mathematics
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    • v.19 no.2
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    • pp.125-140
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    • 2006
  • In 1933, I. Schur introduced a Schur ring in connection with permutation group and regular subgroup. After then, it was studied mostly for purely group theoretical purposes. In 1970s, Klin and Poschel initiated its usage in the investigation of graphs, especially for Cayley and circulant graphs. Nowadays it is known that Schur ring is one of the best way to enumerate Cayley graphs. In this paper we study the origin of Schur ring back to 1933 and keep trace its evolution to graph theory and combinatorics.

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Characteristic polynomials of graph bundles with productive fibres

  • Kim, Hye-Kyung;Kim, Ju-Young
    • Bulletin of the Korean Mathematical Society
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    • v.33 no.1
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    • pp.75-86
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    • 1996
  • Let G be a finite simple connected graph with vertex set V(G) and edge set E(G). Let A(G) be the adjacency matrix of G. The characteristic polynomial of G is the characteristic polynomial $\Phi(G;\lambda) = det(\lambda I - A(G))$ of A(G). A zero of $\Phi(G;\lambda)$ is called an eigenvalue of G.

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The Design of Parallel Routing Algorithm on a Recursive Circulant Network (재귀원형군에서 병렬 경로 알고리즘의 설계)

  • Bae, Yong-Keun;Park, Byung-Kwon;Chung, Il-Yong
    • The Transactions of the Korea Information Processing Society
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    • v.4 no.11
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    • pp.2701-2710
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    • 1997
  • Recursive circulant graph has recently developed as a new model of multiprocessors, and drawn considerable attention to supercomputing, In this paper, we investigate the routing of a message i recursive circulant, that is a key to the performance of this network. On recursive circulant network, we would like to transmit m packets from a source node to a destination node simultaneously along paths, where the ith packet will traverse along the ith path $(o{\leq}i{\leq}m-1)$. In oder for all packets to arrive at the destination node quickly and securely, the ith path must be node-disjoint from all other paths. For construction of these paths, employing the Hamiltonian Circuit Latin Square(HCLS), a special class of $(n{\times}n)$ matrices, we present $O(n^2)$ parallel routing algorithm on recursive circulant network.

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