Let G be a finite group. A simple undirected graph \(\Gamma _{G}^{RI}\) is called a result involution graph of G if the vertex set of \(\Gamma _{G}^{RI}\) is the whole group G and two distinct vertices are adjacent if their product is an involution in G. In this paper, some properties of \(\Gamma _{G}^{RI}\) are obtained. We show that \(\Gamma _{G}^{RI}\) is a connected graph if and only if G is generated by some involutions, \(\Gamma _{G}^{RI}\) is a complete graph if and only if G is an elementary abelian 2-group, and \(\Gamma _{G}^{RI}\) is a complete bipartite graph if and only if \(G=M\rtimes T\) , where M is a abelian group of odd order, \(|T|=2\) and \(C_M(T)=1\) . Finally, we also determine the structure of \(\Gamma _{G}^{RI}\) when G is a finite 2-group which possesses a cyclic maximal subgroup.
