Degree diameter problem

In graph theory, the degree diameter problem is the problem of finding the largest possible graph G (in terms of the size of its vertex set V) of diameter k such that the largest degree of any of the vertices in G is at most d. The size of G is bounded above by the Moore bound; for 1 < k and 2 < d only the Petersen graph, the Hoffman-Singleton graph, and maybe a graph of diameter k = 2 and degree d = 57 attain the Moore bound. In general the largest degree-diameter graphs are much smaller in size than the Moore bound.

See also [edit]

• Cage (graph theory)
• Table of degree diameter graphs
• Table of vertex-symmetric degree diameter digraphs
• Maximum degree-and-diameter-bounded subgraph problem

References [edit]

• Bannai, E.; Ito, T. (1973), "On Moore graphs", J. Fac. Sci. Univ. Tokyo Ser. A 20: 191–208, MR 0323615 

• Hoffman, Alan J.; Singleton, Robert R. (1960), "Moore graphs with diameter 2 and 3", IBM Journal of Research and Development 5 (4): 497–504, doi:10.1147/rd.45.0497, MR 0140437 

• Singleton, Robert R. (1968), "There is no irregular Moore graph", American Mathematical Monthly (Mathematical Association of America) 75 (1): 42–43, doi:10.2307/2315106, MR 0225679 

• Miller, Mirka; Širáň, Jozef (2005), "Moore graphs and beyond: A survey of the degree/diameter problem", Electronic Journal of Combinatorics, Dynamic survey: DS14 

• CombinatoricsWiki - The Degree/Diameter Problem