2-Isomorphic Graphs
2-Isomorphic Graphs
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DOI：
10.1007/978-1-4612-2972-8_8
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发表时间：
1933
影响因子：
1.7
通讯作者：
H. Whitney
中科院分区：
文献类型：
--
作者：
H. Whitney
1.在前文中我们曾说过，如果图G和G '中的一个图可以通过下列两种运算变换为另一个图，则G和G'是2·同构的：（2）图中分支的排列被改变。(3)如果G= H1 + H2，其中H1和H2只有公共顶点a和B，并且这些顶点在H和H2中都是连通的，那么H1在这些顶点处是翻转的。如果G和G '是2-同构的，那么一个图中的任何回路对应于另一个图中的回路;因为任何一种类型的运算都将任何回路变换为回路。在III定理2中证明，如果两个三连通图的弧之间存在1-1对应，使得圈对应于圈，则这两个图是同构的（我们以前使用术语”全等”）。问题来了，对于任何两个图，如果两个图中的回路对应于两个回路，我们可以说什么呢？答案在下面的定理中给出。短语”严格同构（2-iso· morphic）”的意思是：“同构（2-isomorphic），保持图的弧之间的对应。"
1. In the preceding paper we said that two graphs G and G'are 2· isomorphic if one can be transformed into the other by operations of the following two types:(2) The arrangement of the components in the graph is altered.(3) If G= Hl+ H2, where Hl and H2 have just the vertices a and b in common and these vertices are connected in both H land H 2, then Hl is turned around at these vertices.If G and G'are 2-isomorphic, then any circuit in one graph corresponds to a circuit in the other; for an operation of either type transforms any circuit into a circuit. It was shown in III, Theorem 2, t that if there is a 1-1 correspondence between the arcs of two triply connected graphs so that circuits correspond to circuits, § then the two graphs are isomorphic (we formerly used the term" congruent"). The question arises, what can be said about any two graphs in which circuits correspond to circuits? The answer is given in the following theorem. The phrase" strictly isomorphic (2-iso· morphic)" means:" isomorphic (2-isomorphic), preserving the correspondence between the arcs of the graphs."