The Embedding of Line Graphs Associated to the Annihilator Graphs of Commutative Rings

The annihilator graph [Formula: see text] of the commutative ring [Formula: see text] is an undirected simple graph whose vertex set is the set of non-zero zero-divisors of [Formula: see text], and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. In this paper, we study the embedding of the line graph of [Formula: see text] into orientable or non-orientable surfaces. We completely characterize the finite commutative rings such that the line graph of [Formula: see text] is of genus or crosscap at most two. We also obtain the inner vertex number of the line graph of [Formula: see text]. Finally, we classify all the finite commutative rings such that the book thickness of certain line graphs of [Formula: see text] is at most four.