Spanning Trees in Grid Graphs
نویسنده
چکیده
X iv :0 80 9. 25 51 v1 [ m at h. C O ] 1 5 Se p 20 08 Spanning Trees in Grid Graphs Paul Raff July 25, 2008 Abstract A general method is obtained for finding recurrences involving the number of spanning trees of grid graphs, obtained by taking the graph product of an arbitrary graph and path or cycle. The results in this paper extend the work by Desjarlais and Molina and give concrete methods for finding the recurrences. Many new recurrences are found, yielding conjectures on the order of the linear recurrences of grid graphs and graphs obtained by taking the product of a complete graph and a path.
منابع مشابه
Counting the number of spanning trees of graphs
A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.
متن کاملNUMBER OF SPANNING TREES FOR DIFFERENT PRODUCT GRAPHS
In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...
متن کاملMaximum Leaf Spanning Tree Problem for Grid Graphs
The complexity of the maximum leaf spanning tree problem for grid graphs is currently unknown. We determine the maximum number of leaves in a grid graph with up to 4 rows and with 6 rows. Furthermore, we give some constructions of spanning trees of grid graphs with a large number of leaves.
متن کاملDiploma Thesis Minimum Stretch Spanning Trees
Spanning trees have always been of great interest in various areas of computer science. The same is true for the idea of shortest paths in a graph. Minimum Stretch Spanning Trees can be described as a combination of these two concepts. On the one hand they are spanning trees, on the other hand they have a minimum stretch which means that the distances between the nodes in the spanning tree rema...
متن کاملOptimal Self-healing of Smart Distribution Grids Based on Spanning Trees to Improve System Reliability
In this paper, a self-healing approach for smart distribution network is presented based on Graph theory and cut sets. In the proposed Graph theory based approach, the upstream grid and all the existing microgrids are modeled as a common node after fault occurrence. Thereafter, the maneuvering lines which are in the cut sets are selected as the recovery path for alternatives networks by making ...
متن کامل