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Below is the table of the vertex numbers for the best-known graphs (as of July 2022) in the undirected degree diameter problem for graphs of degree at most 3 ≤ d ≤ 16 and diameter 2 ≤ k ≤ 10. Only a few of the graphs in this table (marked in bold) are known to be optimal (that is, largest possible).
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 possibly graphs (not yet proven to exist) 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.
The first number in this sequence, 7, is the degree of the Hoffman–Singleton graph, and the McKay–Miller–Širáň graph of degree seven is the Hoffman–Singleton graph. [2] The same construction can also be applied to degrees d {\displaystyle d} for which ( 2 d + 1 ) / 3 {\displaystyle (2d+1)/3} is a prime power but is 0 or −1 mod 4.
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Every connected graph is an expander; however, different connected graphs have different expansion parameters. The complete graph has the best expansion property, but it has largest possible degree. Informally, a graph is a good expander if it has low degree and high expansion parameters.
Valve's Source game engine uses the Hammer unit as its base unit of length. This unit refers to Source's official map creation software, Hammer. [1] The exact definition varies from game to game, but a Hammer unit is usually defined as a sixteenth of a foot (16 Hammer units = 1 foot).
Likewise, anyone that plans to claim Social Security at age 62 (i.e., as soon as possible) may want to reconsider. That decision results in the most severe benefit reduction.
Alijah Martin scored 18 points, Denzel Aberdeen added 16 and No. 8 Florida thumped top-ranked Tennessee 73-43 on Tuesday night to knock off the last unbeaten team in Division I basketball. Alex ...