CAJ | 학술논문

对于无多重弧的竹阶赋权有向图，引入距离矩阵A，将此矩阵看作取大一加代数（RU{-∞}，max，＋）上的矩阵，证明了只要任一回路的权非正，则A^（n-1）的分量a（tj,^（tt-1））就是顶点i到j的最长距离，且此最长距离必在某条路径上取得。
대우무다중호적죽계부권유향도，인입거리구진A，장차구진간작취대일가대수（RU{-∞}，max，＋）상적구진，증명료지요임일회로적권비정，칙A^（n-1）적분량a（tj,^（tt-1））취시정점i도j적최장거리，차차최장거리필재모조로경상취득。
For an n-th order weighted directed graph without multi-arcs, the distance matrix A is introduced and regarded as one over the max-plus algebra （RU{-∞},max,＋）, and it is proved that if theweight of every cycle is non-positive then the entry a（tj,^（tt-1）） of A^（n-1） is the longest distance from the ver-tex i to the vertex j,and the longest distance is affirmatively obtained on some route.