The contraction method for counting the complexity of planar graphs with cut vertices

Dounia Lotfi, Mohamed El Marraki, Driss Aboutajdine
2013 Applied Mathematical Sciences  
In this paper, we investigate the number of spanning trees in planar graphs with two cut vertices. We propose a combinatorial approach based on the contraction method, in order to derive spanning trees recursions for this class of graphs. Applications on different graphs showed the efficiency and the simplicity of our recursive approach in comparison with the classic matrix tree theorem. Mathematics Subject Classification: 05C85, 05C30
doi:10.12988/ams.2013.34227 fatcat:ttxb2xwxh5adhj2ge6o6h3wlri