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For instance, in the octahedron graph, shown in the figure, each vertex has a neighbourhood isomorphic to a cycle of four vertices, so the octahedron is locally C 4. For example: Any complete graph K n is locally K n-1. The only graphs that are locally complete are disjoint unions of complete graphs. A Turán graph T(rs,r) is locally T((r-1)s,r ...
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex exactly once. A Hamiltonian path that starts and ends at adjacent vertices can be completed by adding ...
This is also known as the vertex 1-center problem and can be extended to the vertex k-center problem. Finding the center of a graph is useful in facility location problems where the goal is to minimize the worst-case distance to the facility. For example, placing a hospital at a central point reduces the longest distance the ambulance has to ...
For example, the edges worksheet contains a minimum of two columns, and each row has a minimum of two elements corresponding to the two vertices that make up an edge in the graph. Graph metrics and edge and vertex visual properties appear as additional columns in the respective worksheets.
The algorithm may be modified to start with any particular vertex s by setting C[s] to be a number smaller than the other values of C (for instance, zero), and it may be modified to only find a single spanning tree rather than an entire spanning forest (matching more closely the informal description) by stopping whenever it encounters another ...
A semi-symmetric graph is a graph that is edge-transitive but not vertex-transitive. A half-transitive graph is a graph that is vertex-transitive and edge-transitive but not symmetric. A skew-symmetric graph is a directed graph together with a permutation σ on the vertices that maps edges to edges but reverses the direction of each edge.