A Formula for the Number of Spanning Trees of a Multi-Star Related Graph

Abstract Using a new labeling technique and matrix computations, this paper derives a closed formula for the number of spanning trees of a multi-star related graph G = K n − K m ( a 1 , a 2 ,…, a m ), where K m ( a 1 , a 2 ,…, a m ) consists of m star graphs such that the i th one has a root node connected to a i leaves, and further, the m roots are connected together to form a complete graph. This result generalizes the previous result by Nikolopoulos and Rondogiannis (1998) which is limited to m = 2, 3, 4.