The number of spanning trees in odd valent circulant graphs

In this paper, we consider the number of spanning trees in circulant graphs. For any class of odd valent circulant graphs <f>C2n(a1,a2,…,ak−1,n)</f>, where <f>a1,a2,…,ak−1</f> are fixed jumps and <f>n</f> varies, some formulas, asymptotic behaviors and linear recurrence relations for the number of its spanning trees are obtained, and some known results on the ones in even valent circulant graphs <f>Cn(a1,a2,…,ak)</f> are improved. [Copyright &y& Elsevier]