Isomorphism Checking of I-graphs

We consider the class of I-graphs, which is a generalization of the class of the generalized Petersen graphs. We show that two I-graphs I(n, j, k) and I(n, j ₁, k ₁) are isomorphic if and only if there exists an integer a relatively prime to n such that either {j ₁, k ₁} =? {a j mod n, a k mod n } or {j ₁, k ₁} =? {a j mod n, ? a k mod n }. This result has an application in the enumeration of non-isomorphic I-graphs and unit-distance representations of generalized Petersen graphs.