Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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경쟁그래프와 경쟁수에 대하여

  • 김서령 (경희대학교 이학부 수학전공)
  • Published : 2001.01.01
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Abstract

어떤 유향그래프 D의 경쟁그래프란 D와 같은 꼭지점들의 집합을 갖고 두 개의 꼭지점 x와 y가 변으로 연결되어있는 것과 동치인 조건이 D에서 어떤 꼭지점 z에 대하여 유향변(x,z)와 (y,z)가 존재하는 것인 그래프로 정의된다. 어떤 그래프 G의 경쟁수란 G에 첨가하여 생기는 그래프가 유향 회로가 없는 유향그래프의 경쟁그래프가 되도록 하는 고립된 꼭지점의 최소수로 정의된다. 갱쟁그래프의 개념은 생태학적 위상공간의 최소차원을 결정하는 수단으로 1968에 Cohen에 의하여 도입되었다. 경쟁그래프와 그것의 변형들은 잡음이 많은 통신로 상에서의 교신, 라디오 송신기에 주파수 부어하기, 복잡한 경제 체계와 에너지 체계에 응용된다. 이 논문에서는 경쟁 그래프와 그 변형들, 경쟁수와 그 변형들에 대하여 소개하며 그것들에 대한 중요한 결과들을 개관하고 미해결 문제들을 제시하고자 한다.

Keywords

References

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