On the number of spanning trees of a multi-complete/star related graph

Abstract This paper derives a closed formula for the number of spanning trees of a multi-complete/star related graph G=K n −K m (a 1 ,a 2 ,…,a l ;b 1 ,b 2 ,…,b m−l ) , where K m (a 1 ,a 2 ,…,a l ;b 1 ,b 2 ,…,b m−l ) consists of l complete graphs and m−l star graphs such that the i th complete graph has a i +1 nodes; the j th star graph has b j +1 nodes, and further, the related m roots are connected together to form a complete graph. The proposed results extend previous results to a larger graph class. In addition, we provide a general maximization theorem for the multi-star graph.