The number of spanning trees in a superprism

Abstract

Let the vertices of two disjoint and equal length cycles be denoted u 0 , u 1 , . . . , u n − 1 in the first cycle and v 0 , v 1 , . . . , v n − 1 in the second cycle for n ≥ 4 . The superprism ˘ P n is defined as the graph obtained by adding to these disjoint cycles all edges of the form u i v i and u i v i +2 (mod n ) . In this paper, it is proved that the number of spanning trees in ˘ P n is n · 2 3 n − 2 .