Commuting Involution Graphs for 4-Dimensional Projective Symplectic Groups

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 and X a G-conjugacy class of involutions, determining the diameters and structure of the discs of these graphs