Minimum cycle bases of product graphs
نویسندگان
چکیده
A construction for a minimal cycle basis for the Cartesian and the strong product of two graphs from the minimal length cycle bases of the factors is presented. Furthermore, we derive asymptotic expressions for the average length of the cycles in the minimal cycle bases of the powers (iterated products) of graphs. In the limit only triangles and squares play a role.
منابع مشابه
Minimum cycle bases of lexicographic products
Minimum cycle bases of product graphs can in most situations be constructed from minimum cycle bases of the factors together with a suitable collection of triangles and/or quadrangles determined by the product operation. Here we give an explicit construction for the lexicographic product G ◦ H that generalizes results by Berger and Jaradat to the case that H is not connected.
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We construct a minimum cycle basis for the direct product K2 × Kp of two complete graphs where p ≥ 2. For p > 3, these bases consists only of squares. This completes the work of R. Hammack, who treated the case Kp ×Kq for p, q ≥ 3 [Inform. Process. Lett. 102 (2007), 214–218.]
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 26 شماره
صفحات -
تاریخ انتشار 2002