Applying a combinatorial determinant to count weighted cycle systems in a directed graph |
| |
Authors: | Christopher R.H. Hanusa |
| |
Affiliation: | Department of Mathematical Sciences, Binghamton University, Binghamton, NY, USA |
| |
Abstract: | One method for counting weighted cycle systems in a graph entails taking the determinant of the identity matrix minus the adjacency matrix of the graph. The result of this operation is the sum over cycle systems of −1 to the power of the number of disjoint cycles times the weight of the cycle system. We use this fact to reprove that the determinant of a matrix of much smaller order can be computed to calculate the number of cycle systems in a hamburger graph. |
| |
Keywords: | Cycle system Cycle cover Hamburger graph Hamburger matrix Determinant Directed graph |
本文献已被 ScienceDirect 等数据库收录! |