On \(\pi \) -Product Involution Graphs in Symmetric Groups

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• 作者：Peter Rowley ; David Ward
• 刊名：Graphs and Combinatorics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：32
• 期：4
• 页码：1545-1570
• 全文大小：1,664 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Engineering Design
  
• 出版者：Springer Japan
• ISSN：1435-5914
• 卷排序：32

文摘

Suppose that G is a group, X a subset of G and \(\pi \) a set of natural numbers. The \(\pi \)-product graph \(\mathcal {P}_{\pi }(G,X)\) has X as its vertex set and distinct vertices are joined by an edge if the order of their product is in \(\pi \). If X is a set of involutions, then \(\mathcal {P}_{\pi }(G,X)\) is called a \(\pi \)-product involution graph. In this paper we study the connectivity and diameters of \(\mathcal {P}_{\pi }(G,X)\) when G is a finite symmetric group and X is a G-conjugacy class of involutions.KeywordsSymmetric groupProductGraphDiameterConnectedness