An upper limit on the number of nodes in a regular graph of degree d>2 and diameter k:
N(d,k) <= d(d-1)^k - 2 ------------ d-2
[moo r] /mʊər/ verb (used with object) 1. to secure (a ship, boat, dirigible, etc.) in a particular place, as by cables and anchors or by lines. 2. to fix firmly; secure. verb (used without object) 3. to moor a ship, small boat, etc. 4. to be made secure by cables or the like. noun […]
n. “coffee-room, viewed from the inside through a glass door, as it was seen by Dickens on a dark London day; … used by Chesterton to denote the queerness of things that have become trite, when they are seen suddenly from a new angle.” [J.R.R. Tolkien]
- Moore graph
A graph which achieves the Moore bound. These are complete graphs, polygon graphs (regular graphs of degree 2) and three others: (nodes, degree, diameter) = (10,3,2), (50,7,2) and the possible but undiscovered (3250,57,2).
[moo r-foul] /ˈmʊərˌfaʊl/ noun, plural moorfowls (especially collectively) moorfowl. Chiefly British. 1. the red grouse. /ˈmʊəˌfaʊl; ˈmɔː-/ noun 1. (in British game laws) an archaic name for red grouse Compare heathfowl