The Enumeration of Homeomorphically Irreducible Star Graphs
The Enumeration of Homeomorphically Irreducible Star Graphs
复制标题
同胚不可约星图的枚举
DOI：
10.1063/1.1705068
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发表时间：
1966
期刊：
影响因子：
--
通讯作者：
B. Heap
中科院分区：
文献类型：
--
作者：
B. Heap
在用级数形式表示相互作用系统的性质时，在许多情况下只涉及星星图上的求和。通过将这些图简化为同胚不可约星，从而简化了这些图的识别和分类。这些图可以被视为所有可能的不同拓扑类型的星星。本文描述了一种方法，它已被用来产生所有不同的同胚不可约星的圈数≤ 5。特别地，已经确定有118个圈数为5的这样的图，其中111个是平面的。这些图的图表，并附上了一个表，他们的k权，这是需要获得系列的渗滤过程，也给出了。推广了该方法，计算了8点12边同胚不可约星的个数，并给出了一个表。
In expressing properties of interacting systems in the form of series, in many cases only summation over star graphs is involved. The identification and classification of such graphs is simplified by reducing them to homeomorphically irreducible stars. These graphs can be regarded as being all the possible different topological types of star. A method is described which has been used to produce all the different homeomorphically irreducible stars which have cyclomatic numbers ≤ 5. In particular, it has been established that there are 118 such graphs with cyclomatic number 5, 111 of which are planar. Diagrams of these graphs are appended, and a table of their k weights, which are needed for obtaining series for percolation processes, is also given. An extension of the method has been used to count the numbers of homeomorphically irreducible stars containing up to 8 vertices and 12 edges, a table of which is given.