On minimum vertex covers of generalized Petersen graphs
نویسندگان
چکیده
For natural numbers n and k (n > 2k), a generalized Petersen graph P (n, k), is defined by vertex set {ui, vi} and edge set {uiui+1, uivi, vivi+k}; where i = 1, 2, . . . , n and subscripts are reduced modulo n. Here first, we characterize minimum vertex covers in generalized Petersen graphs. Second, we present a lower bound and some upper bounds for β(P (n, k)), the size of minimum vertex cover of P (n, k). Third, in some cases, we determine the exact values of β(P (n, k)). Our conjecture is that β(P (n, k)) ≤ n+ ⌈ 5 ⌉, for all n and k. 254 B. BEHSAZ, P. HATAMI AND E. S. MAHMOODIAN
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 40 شماره
صفحات -
تاریخ انتشار 2008