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The number of spanning trees in directed circulant graphs with non-fixed jumps. (English) Zbl 1143.05041
The phrase “non-fixed jumps” in the title is somewhat misleading. The author apparently has in mind that the formulas depend on the integer \(n\) which controls the jumps. For example there is given a formula for the number of trees of the circulant graph \(C_{pn}(a_1,\dots,a_k, q_1n,\dots,q_mn)\) using a formula for \(C_n(a_1,\dots,a_k)\) and other functions depending on \(n\). Similarly asymptotic behaviours and linear recurrence relations are considered for this problem. In 10 examples the formulas are evaluated for graphs of the form \(C_{kn}(1,rn)\) with \(k=2,3,4,5,6\) and \(r= 1,2,3,5\) and for \(C_{2n}(1,2,n)\).

MSC:
05C30 Enumeration in graph theory
05C05 Trees
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