## 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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### References:

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