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Let two points x and y be picked randomly from a unit n-dimensional hypercube. The expected distance between the points Delta(n), i.e., the mean line segment length, is then ...

A set of points capable of being enclosed in intervals whose total length is arbitrarily small.

The Möbius-Kantor graph is the unique cubic symmetric graph on 16 nodes, illustrated above in several embeddings. Its unique canonical LCF notation is [5,-5]^8. The ...

An extension of two-valued logic such that statements need not be true or false, but may have a degree of truth between 0 and 1. Such a system can be extremely useful in ...

The rhombic dodecahedral graph is the Archimedean dual graph which is the skeleton of the rhombic dodecahedron (as well as the Bilinski dodecahedron). It is the Levi graph of ...

The m-book graph is defined as the graph Cartesian product B_m=S_(m+1) square P_2, where S_m is a star graph and P_2 is the path graph on two nodes. The generalization of the ...

A kayak paddle graph KP(k,m,l) is the graph obtained by joining cycle graphs C_k and C_m by a path of length l (Gallian 2018). KP(3,3,1) is isomorphic to the 3-barbell graph. ...

Let a chess piece make a tour on an n×n chessboard whose squares are numbered from 1 to n^2 along the path of the chess piece. Then the tour is called a magic tour if the ...

If A moves along a known curve, then P describes a pursuit curve if P is always directed toward A and A and P move with uniform velocities. Pursuit curves were considered in ...

Tutte's fragment (Taylor 1997) is the 15-node graph illustrated above (Grünbaum 2003, pp. 358-359 and Fig. 17.1.3). If the graph obtained by adding pendant edges to corners ...