Chip Removal. Urban Renewal Revisited
We describe a new combinatorial-algebraic transformation on graphs which we call the “chip removal.” It generalizes the well-known urban renewal trick of Propp and Kuperberg. The chip removal is useful in calculations of the determinants of adjacency matrices and matching numbers of graphs. A beautiful example of applying this technique is a theorem on removing 4-contact chips, which generalizes Kuo’s graphical condensation method. Numerous examples are given. Bibliography: 6 titles.
KeywordsAdjacency Matrix Chebyshev Polynomial Urban Renewal Outgoing Edge Adjacency Matrice
Unable to display preview. Download preview PDF.
- 2.K. Bibak and R. Tauraso, “Determinants of grids, tori, cylinders and M¨obius ladders,” arXiv:1212.4816v1.Google Scholar