The number of shortest cycles and the chromatic uniqueness of a graph
The number of shortest cycles and the chromatic uniqueness of a graph
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最短循环数和图的颜色唯一性
DOI：
10.1002/jgt.3190160103
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
K. Koh
中科院分区：
文献类型：
--
作者：
C. Teo;K. Koh
对于图G，令G（G）和σG（G）分别表示G的Girth和G中的长度G（G）的循环数。 g（g）确定σg（g）达到结合的2个相互连接的结构。最终应用于表明某些图的家族在色度上是唯一的
For a graph G, let g(G) and σ g (G) denote, respectively, the girth of G and the number of cycles of length g(G) in G. In this paper, we first obtain an upper bound for σ g (G) and determine the structure of a 2-connected graph G when σ g (G) attains the bound. These extremal graphs are then more-or-less classified, but one case leads to an unsolved problem. The structural results are finally applied to show that certain families of graphs are chromatically unique