Asymptotic Enumeration Theorems for the Numbers of Spanning Trees and Eulerian Trials in Circulant Digraphs & Graphs
نویسندگان
چکیده
In this paper, we consider the asymptotic properties of the numbers of spanning trees and Eulerian trials in circulant digraphs and graphs. Let C(p, s1, s2, . . . , sk) be a directed or undirected circulant graph. Let T (C(p, s1, s2, . . . , sk)) and E(C(p, s1, s2, . . . , sk)) be the numbers ∗This work was partially supported by the Natural Science Foundation of China, email: [email protected] †This work was partially supported by Hong Kong CERG grant HKUST652/95E, email: [email protected] of spanning trees and of Eulerian trials, respectively. Then we have lim p→+∞ 1 k {T (C(p, s1, s2, . . . , sk))} 1 p = 1, lim p→+∞ 1 k! {E(C(p, s1, s2, . . . , sk))} 1 p = 1. Furthermore, we deal with their line digraph and graph iterations respectively, and obtain similar results.
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