1 2 Ju l 2 01 7 On the forcing spectrum of generalized Petersen graphs P ( n , 2 ) ∗
نویسندگان
چکیده
The forcing number of a perfect matching M of a graph G is the smallest cardinality of subsets of M that are contained in no other perfect matchings of G. The forcing spectrum of G is the collection of forcing numbers of all perfect matchings of G. In this paper, we classify the perfect matchings of a generalized Petersen graph P (n, 2) in two types, and show that the forcing spectrum is the union of two integer intervals. For n ≥ 34, it is [ ⌈ n 12⌉+ 1, ⌈ n+3 7 ⌉+ δ(n) ] ∪ [ ⌈ 6 ⌉, ⌈ n 4 ⌉ ] , where δ(n) = 1 if n ≡ 3 (mod 7), and δ(n) = 0 otherwise.
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