Independence numbers of the 2-token graphs of some join graphs - Rivera, Luis Manuel; Vazquez Briones, Gerardo (Boletín de la Sociedad Matemática Mexicana, 2025)
The 2-token graphF2(G) of a graph G is the graph whose set of vertices consists of all the 2-subsets of V(G), where two vertices are adjacent if and only if their symmetric difference is an edge in G. Let G be the join graph of En and H, where H is any graph. In this paper, we give a method to construct an independent set I′ of F2(G) from an independent set I of F2(G) such that |I′|≥|I|. As an application, we obtain the independence number of the 2-token graphs of fan graphs Fn,m, wheel graphs Wn,m and En+Kn.