moore graph การใช้

• The graphs matching this bound were named Moore graphs by.
• Unlike all other Moore graphs, vertex-transitive.
• Moreover, the bounds on the sizes of Moore graphs generalize to cages : any cage with odd girth " g " must have at least
• An equivalent definition of a Moore graph is that it is a graph of diameter " k " with girth 2 " k " + 1.
• If the generalized definition of Moore graphs that allows even girth graphs is used, the even girth Moore graphs correspond to incidence graphs of ( possible degenerate ) Generalized polygons.
• If the generalized definition of Moore graphs that allows even girth graphs is used, the even girth Moore graphs correspond to incidence graphs of ( possible degenerate ) Generalized polygons.
• More generally, it is known (; ) that, other than the graphs listed above, all Moore graphs must have girth 5, 6, 8, or 12.
• This idea was a great challenge for most analysts of the 18th century, and as a result an algorithm was derived from the Moore graph which was later called the Moore Neighborhood algorithm.
• Later, showed that Moore graphs can equivalently be defined as having diameter " k " and girth 2 " k " + 1; these two requirements combine to force the graph to be " d "-regular for some " d " and to satisfy the vertex-counting formula.