On Diameter of Subgraphs of Commuting Graph in Symplectic Group for Elements of Order Three

Suppose G be a finite group and X subset of G. The commuting graph, denoted by C(G,X), is simple undirected where ⊂G being the set vertex two distinct vertices x,y∈X are joined an edge if only xy = yx. aim this paper was to describe structure disconnected graph considering symplectic conjugacy class elements order three. main work discover disc diameter subgraph as well suborbits groups S4(2)', S4(3) S6(2). Additionally, mathematical formulas derived proved, one gives number subgraphs based on size each class, whilst other relying in disc.