Search results
Results from the WOW.Com Content Network
It has 104 edges and 52 vertices and is currently the smallest known example of a 4-regular matchstick graph. [3] It is a rigid graph. [4] Every 4-regular matchstick graph contains at least 20 vertices. [5] Examples of 4-regular matchstick graphs are currently known for all number of vertices ≥ 52 except for 53, 55, 56, 58, 59, 61 and 62.
207 is a Wedderburn-Etherington number. [1] There are exactly 207 different matchstick graphs with eight edges. [2] [3] 207 is a deficient number, as 207's proper divisors (divisors not including the number itself) only add up to 105: + + + + = <.
Every matchstick graph is a planar graph, [14] but some otherwise-planar unit distance graphs (such as the Moser spindle) have a crossing in every representation as a unit distance graph. Additionally, in the context of unit distance graphs, the term 'planar' should be used with care, as some authors use it to refer to the plane in which the ...
The number of perfect matchings in a complete graph K n (with n even) is given by the double factorial (n − 1)!!. [13] The numbers of matchings in complete graphs, without constraining the matchings to be perfect, are given by the telephone numbers. [14] The number of perfect matchings in a graph is also known as the hafnian of its adjacency ...
The matching polynomial of a graph G with n vertices is related to that of its complement by a pair of (equivalent) formulas. One of them is a simple combinatorial identity due to Zaslavsky (1981). The other is an integral identity due to Godsil (1981). There is a similar relation for a subgraph G of K m,n and its complement in K m,n. This ...
Graph coloring [2] [3]: GT4 Graph homomorphism problem [3]: GT52 Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph.
Pages in category "Geometric graphs" The following 34 pages are in this category, out of 34 total. ... Matchstick graph; N. Nearest neighbor graph; P.
For sparse bipartite graphs, the maximum matching problem can be solved in ~ (/) with Madry's algorithm based on electric flows. [3] For planar bipartite graphs, the problem can be solved in time O(n log 3 n) where n is the number of vertices, by reducing the problem to maximum flow with multiple sources and sinks. [4]