• 제목/요약/키워드: k-connected graph

검색결과 145건 처리시간 0.027초

A LOWER BOUND FOR THE CONVEXITY NUMBER OF SOME GRAPHS

  • Kim, Byung-Kee
    • Journal of applied mathematics & informatics
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    • 제14권1_2호
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    • pp.185-191
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    • 2004
  • Given a connected graph G, we say that a set EC\;{\subseteq}\;V(G)$ is convex in G if, for every pair of vertices x, $y\;{\in}\;C$, the vertex set of every x - y geodesic in G is contained in C. The convexity number of G is the cardinality of a maximal proper convex set in G. In this paper, we show that every pair k, n of integers with $2\;{\leq}k\;{\leq}\;n\;-\;1$ is realizable as the convexity number and order, respectively, of some connected triangle-free graph, and give a lower bound for the convexity number of k-regular graphs of order n with n > k+1.

CLASSIFICATION OF TWO-REGULAR DIGRAPHS WITH MAXIMUM DIAMETER

  • Kim, Byeong Moon;Song, Byung Chul;Hwang, Woonjae
    • Korean Journal of Mathematics
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    • 제20권2호
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    • pp.247-254
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    • 2012
  • The Klee-Quaife problem is finding the minimum order ${\mu}(d,c,v)$ of the $(d,c,v)$ graph, which is a $c$-vertex connected $v$-regular graph with diameter $d$. Many authors contributed finding ${\mu}(d,c,v)$ and they also enumerated and classied the graphs in several cases. This problem is naturally extended to the case of digraphs. So we are interested in the extended Klee-Quaife problem. In this paper, we deal with an equivalent problem, finding the maximum diameter of digraphs with given order, focused on 2-regular case. We show that the maximum diameter of strongly connected 2-regular digraphs with order $n$ is $n-3$, and classify the digraphs which have diameter $n-3$. All 15 nonisomorphic extremal digraphs are listed.

EXTREMAL ATOM-BOND CONNECTIVITY INDEX OF CACTUS GRAPHS

  • ASHRAFI, ALI REZA;DEHGHAN-ZADEH, TAYEBEH;HABIBI, NADER
    • 대한수학회논문집
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    • 제30권3호
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    • pp.283-295
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    • 2015
  • The atom-bond connectivity index of a graph G (ABC index for short) is defined as the summation of quantities $\sqrt{\frac{d(u)+d(v)-2}{d(u)d(v)}}$ over all edges of G. A cactus graph is a connected graph in which every block is an edge or a cycle. The aim of this paper is to obtain the first and second maximum values of the ABC index among all n vertex cactus graphs.

텐던 구동 로봇 메커니즘의 일반화된 그래프 표현 (Generalized Graph Representation of Tendon Driven Robot Mechanism)

  • 조영수;정주노;김두형
    • 로봇학회논문지
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    • 제9권3호
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    • pp.178-184
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    • 2014
  • Tendon driven robot mechanisms have many advantages such as allowing miniaturization and light-weight designs and/or enhancing flexibility in the design of structures. When designing or analyzing tendon driven mechanisms, it is important to determine how the tendons should be connected and whether the designed mechanism is easily controllable. Graph representation is useful to view and analyze such tendon driven mechanisms that are complicatedly interconnected between mechanical elements. In this paper, we propose a method of generalized graph representation that provides us with an intuitive analysis tool not only for tendon driven manipulators, but also various other kinds of mechanical systems which are combined with tendons. This method leads us to easily obtain structure matrix - which is the one of the most important steps in analyzing tendon driven mechanisms.

AN IDEAL-BASED ZERO-DIVISOR GRAPH OF 2-PRIMAL NEAR-RINGS

  • Dheena, Patchirajulu;Elavarasan, Balasubramanian
    • 대한수학회보
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    • 제46권6호
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    • pp.1051-1060
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    • 2009
  • In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact $T_1$-subspace. We also study the zero-divisor graph $\Gamma_I$(R) with respect to the completely semiprime ideal I of N. We show that ${\Gamma}_{\mathbb{P}}$ (R), where $\mathbb{P}$ is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph ${\Gamma}_{\mathbb{P}}$ (R).

MONOPHONIC PEBBLING NUMBER OF SOME NETWORK-RELATED GRAPHS

  • AROCKIAM LOURDUSAMY;IRUDAYARAJ DHIVVIYANANDAM;SOOSAIMANICKAM KITHER IAMMAL
    • Journal of applied mathematics & informatics
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    • 제42권1호
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    • pp.77-83
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    • 2024
  • Chung defined a pebbling move on a graph G as the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The monophonic pebbling number guarantees that a pebble can be shifted in the chordless and the longest path possible if there are any hurdles in the process of the supply chain. For a connected graph G a monophonic path between any two vertices x and y contains no chords. The monophonic pebbling number, µ(G), is the least positive integer n such that for any distribution of µ(G) pebbles it is possible to move on G allowing one pebble to be carried to any specified but arbitrary vertex using monophonic a path by a sequence of pebbling operations. The aim of this study is to find out the monophonic pebbling numbers of the sun graphs, (Cn × P2) + K1 graph, the spherical graph, the anti-prism graphs, and an n-crossed prism graph.

제약 조건을 갖는 버블정렬 그래프의 연결도 분석 (Analysis of Bubblesort graph's connectivity which has a conditions for limitations)

  • 서정현;이형옥
    • 한국정보통신학회:학술대회논문집
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    • 한국정보통신학회 2017년도 춘계학술대회
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    • pp.321-324
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    • 2017
  • 버블정렬 그래프는 자료를 정렬하는 버블정렬 기법을 수학적 모델인 그래프로 모델링한 것이다. 버블정렬 그래프 Bn는 분지수 n, 라우팅 경로 길이 ${\frac{n(n-1)}{2}}$, 망비용 $O(n^3)$이다. 본 연구에서는 버블정렬 그래프의 망비용을 개선하기 위한 방법으로 버블정렬 그래프의 분지수 개수를 대략 ${\frac{1}{2}}$ 정도 줄인 제약조건을 제시한다. 이러한 제약 조건을 갖는 버블정렬 그래프는 임의의 노드 U에서 V까지 라우팅을 위해 연결된 그래프임을 증명한다.

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CERTAIN GENERALIZED THORN GRAPHS AND THEIR WIENER INDICES

  • Kathiresan, KM.;Parameswaran, C.
    • Journal of applied mathematics & informatics
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    • 제30권5_6호
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    • pp.793-807
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    • 2012
  • If G is any connected graph of order p; then the thorn graph $G_p^*$ with code ($n_1$, $n_2$, ${\cdots}$, $n_p$) is obtained by adding $n_i$ pendent vertices to each $i^{th}$ vertex of G. By treating the pendent edge of a thorn graph as $P_2$, $K_2$, $K_{1,1}$, $K_1{\circ}K_1$ or $P_1{\circ}K_1$, we generalize a thorn graph by replacing $P_2$ by $P_m$, $K_2$ by $K_m$, $K_{1,1}$ by $K_{m,n}$, $K_1{\circ}K_1$ by $K_m{\circ}K_1$ and $P_1{\circ}K_1$ by $P_m{\circ}K_1$ and their respective generalized thorn graphs are denoted by $G_P$, $G_K$, $G_B$, $G_{KK}$ and $G_{PK}$ respectively. Many chemical compounds can be treated as $G_P$, $G_K$, $G_B$, $G_{KK}$ and $G_{PK}$ of some graphs in graph theory. In this paper, we obtain the bounds of the wiener index for these generalization of thorn graphs.

지상 로봇의 분산형 임무할당과 무인기의 네트워크 연결성 추정 및 제어를 통한 협업 (Cooperation with Ground and Arieal Vehicles for Multiple Tasks: Decentralized Task Assignment and Graph Connectivity Control)

  • 문성원;김현진
    • 제어로봇시스템학회논문지
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    • 제18권3호
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    • pp.218-223
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    • 2012
  • Maintenance and improvement of the graph connectivity is very important for decentralized multi-agent systems. Although the CBBA (Consensus-Based Bundle Algorithm) guarantees suboptimal performance and bounded convergence time, it is only valid for connected graphs. In this study, we apply a decentralized estimation procedure that allows each agent to track the algebraic connectivity of a time-varying graph. Based on this estimation, we design a decentralized gradient controller to maintain the graph connectivity while agents are traveling to perform assigned tasks. Simulation result for fully-actuated first-order agents that move in a 2-D plane are presented.

불완전명세 상태천이그래프상에서 미정의상태를 이용한 동기순차회로의 테스트용이화 합성 (Synthesis for Testability of Synchronous Sequential Circuits Using Undefined States on Incompletely-Specified State Transition Graph)

  • 최호용;김수현
    • 대한전자공학회논문지SD
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    • 제42권10호
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    • pp.47-54
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    • 2005
  • 본 논문에서는 불완전명세(incompletely-specified)를 가진 상태전이그래프(state transition graph: STG)상에서 리던던트 고장(redundant faults)수를 줄여 테스트를 용이하게 하기 위한 새로운 동기 순차회로의 합성방법을 제안한다. 이 STG 합성법에는 1) 구별전이(distinguishable transition)을 이용하여 무정의상태(undefined states)와 불완전명세된 입력전이를 추가하고, 2) 가능한 한 강연결(strongly-connected)이 되도록 하는 방법을 사용한다. 제안된 방법을 이용하여 MCNC 벤치마크 회로에 대해 실험한 결과, 대부분의 회로에 대해 무해 고장의 수가 현격히 줄어들어 높은 고장검출을 얻었다.