Isomorphism checking of I-graphs
Tomaž Pisanski, Boris Horvat and Arjana Žitnik
Graphs and combinatorics 2011. ISSN 0911-0119

Abstract

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.

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