论文摘要
设图G是一个简单图.图G的线图L（G）以图G的边集作为顶点集, L（G）的两个顶点相邻当且仅当它们在图G中相邻.Chartrand等[2]引进了一类变换图Jk（G）,称作图G的k-跳图. Jk（G）的顶点集为G的所有k条边的子图构成;两个顶点H和F在Jk（G）中相邻当且仅当G中存在四个不同的顶点u, v, w和x使得uv∈E（F）, wx∈E（G）?E（F）并且H = F ?uv+wx.显然, J1（G） = L（G）,并J1（G）被称作跳图.事实上,跳图有许多很好的性质,例如它的直径很小而连通度却很大. Chartrand等[2]证明了一个连通的跳图的直径不超过4. Wu和Meng [12]证明了一个连通的跳图的连通度至少比它的最小度小1,并给出了一个跳图是哈密尔顿的充要条件. Wu等[11]给出了一个图G的跳图分别是Supper-connected和hyper-connected跳图的充要条件. H′ector Hevia等人在文献[5]中刻画了所有的平面图J2（G）. Chartrand等[3]刻画了迭跳图的平面性. 2004年Wei和Liu [10]刻画了平面的3,4-跳图的平面.本文中,我们给出了跳图为平面图的充要条件.本文分为两章,第一章是引言部分,介绍了文章的基本概念、背景和主要结果.第二章是定理的证明部分,分为两节.第一节介绍了本文用到的定理及推论.第二节是定理的详细证明过程.
论文目录
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