On commuting graphs for elements of order 3 in symmetric groups. (English) Zbl 1307.05111
Summary: The commuting graph \(\mathcal{C}(G,X)\), where \(G\) is a group and \(X\) is a subset of \(G\), is the graph with vertex set \(X\) and distinct vertices being joined by an edge whenever they commute. Here the diameter of \(\mathcal{C}(G,X)\) is studied when \(G\) is a symmetric group and \(X\) a conjugacy class of elements of order \(3\).
MSC:
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
| 05C12 | Distance in graphs |
| 20B30 | Symmetric groups |
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