• 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.