Commuting Involution Graphs for 4-Dimensional Projective Symplectic Groups

Source abstract

Abstract For a group G and X a subset of G the commuting graph of G on X , denoted by $$\mathcal {C}(G,X)$$ C ( G , X ) , is the graph whose vertex set is X with $$x,y\in X$$ x , y ∈ X joined by an edge if $$x\ne y$$ x ≠ y and x and y commute. If the elements in X are involutions, then $$\mathcal {C}(G,X)$$ C ( G , X ) is called a commuting involution graph. This paper studies $$\mathcal {C}(G,X)$$ 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.