• Commuting Involution Graphs for 4-Dimensional Projective Symplectic Groups

      Everett, Alistaire; Rowley, Peter; email: peter.j.rowley@manchester.ac.uk (Springer Japan, 2020-06-04)
      Abstract: For a group G and X a subset of G the commuting graph of G on X, denoted by C(G, X), is the graph whose vertex set is X with x, y∈X joined by an edge if x≠y and x and y commute. If the elements in X are involutions, then C(G, X) is called a commuting involution graph. This paper studies C(G, X) when G is a 4-dimensional projective symplectic group over a finite field and X a G-conjugacy class of involutions, determining the diameters and structure of the discs of these graphs.
    • Commuting Involution Graphs for Certain Exceptional Groups of Lie Type

      Aubad, Ali; Rowley, Peter; orcid: 0000-0002-3044-7271; email: peter.j.rowley@manchester.ac.uk (Springer Japan, 2021-05-16)
      Abstract: Suppose that G is a finite group and X is a G-conjugacy classes of involutions. The commuting involution graph C(G, X) is the graph whose vertex set is X with x, y∈X being joined if x≠y and xy=yx. Here for various exceptional Lie type groups of characteristic two we investigate their commuting involution graphs.