Cayley subspace sum graph of vector spaces

Let $\mathbb{V}$ be a finite dimensional vector space over the field $\mathbb{F}$. $S(\mathbb{V})$ set of all subspaces and $\mathbb{A}\subseteq S^*(\mathbb{V})=S(\mathbb{V})\backslash\{0\}.$ In this paper, we define Cayley subspace sum graph $\mathbb{V},$ denoted by Cay$(S^*(\mathbb{V}),\mathbb{A}), $ as simple undirected with vertex $S^*(\mathbb{V})$ two distinct vertices $X$ $Y$ are adjacent if $X+Z=Y$ or $Y+Z=X$ for some $Z\in \mathbb{A}$. Having defined graph, study about connectedness, diameter girth several classes graphs Cay$(S^*(\mathbb{V}), \mathbb{A})$