The strongly distance-balanced property of the generalized Petersen graphs
DOI:
https://doi.org/10.26493/1855-3974.75.895Keywords:
graph, strongy distance-balanced, generalized Petersen graphAbstract
A graph X is said to be strongly distance-balanced whenever for any edge uv of X and any positive integer i, the number of vertices at distance i from u and at distance i + 1 from v is equal to the number of vertices at distance i + 1 from u and at distance i from v. It is proven that for any integers k ≥ 2 and n ≥ k2 + 4k + 1, the generalized Petersen graph GP(n, k) is not strongly distance-balanced.Downloads
Published
2009-01-25
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