吳森原李世仁2014-10-272014-10-271982-06-??http://rportal.lib.ntnu.edu.tw/handle/20.500.12235/17108STEPHEN B. MAURER [3] 曾討論到圖形中頂點著色不具孤立點(vertex-coloring without isolates)的性質。在本文中我們將此性質應用到圖形邊著色上稱為邊著色不具孤立邊(edge-coloring without isolates)，並分別應用到平面地圖與球面圖上，稱為區著色不具孤立區(region-coloring without isolates)，且更深遠地討論到圖形G的每一階線圖形Ln(G)上。S.B. Maurer [3] has studied the properties of vertex coloring without isolates in graph. In this paper, we use these concepts to study the properties of edge-coloring without isolates in a graph and apply it to plane graphs and sphere graphs, called region coloring without isolates. Furthermore, we also study these properties in any order of line graph Ln(G)區著色頂點邊