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Commuting Involution Graphs for 4-Dimensional Projective Symplectic GroupsAbstract: 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.