Diameter of generalized Petersen graphs

Due to their broad application to different fields of theory and practice, generalized Petersen graphs GPG(n, s) have been extensively investigated. Despite the regularity of generalized Petersen graphs, determining an exact formula for the diameter is still a difficult problem. In their paper, Beenker and Van Lint have proved that if the circulant graph Cn(1, s) has diameter d, then GPG(n, s) has diameter at least d + 1 and at most d + 2. In this paper, we provide necessary and sufficient conditions so that the diameter of GPG(n, s) is equal to d+1, and sufficient conditions so that the diameter of GPG(n, s) is equal to d+ 2. Afterwards, we give exact values for the diameter of GPG(n, s) for almost all cases of n and s. Furthermore, we show that there exists an algorithm computing the diameter of generalized Petersen graphs with running time O(logn).

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