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A graceful labeling (or graceful numbering) is a special graph labeling of a graph on m edges in which the nodes are labeled with a subset of distinct nonnegative integers ...

A graph G is hypohamiltonian if G is nonhamiltonian, but G-v is Hamiltonian for every v in V (Bondy and Murty 1976, p. 61). The Petersen graph, which has ten nodes, is the ...

An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor ...

The Klein bottle is a closed nonorientable surface of Euler characteristic 0 (Dodson and Parker 1997, p. 125) that has no inside or outside, originally described by Felix ...

A line graph L(G) (also called an adjoint, conjugate, covering, derivative, derived, edge, edge-to-vertex dual, interchange, representative, or theta-obrazom graph) of a ...

A number is said to be simply normal to base b if its base-b expansion has each digit appearing with average frequency tending to b^(-1). A normal number is an irrational ...

The m×n queen graph Q_(m,n) is a graph with mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a queen. ...

Spherical coordinates, also called spherical polar coordinates (Walton 1967, Arfken 1985), are a system of curvilinear coordinates that are natural for describing positions ...

A strong pseudoprime to a base a is an odd composite number n with n-1=d·2^s (for d odd) for which either a^d=1 (mod n) (1) or a^(d·2^r)=-1 (mod n) (2) for some r=0, 1, ..., ...

A k-regular simple graph G on nu nodes is strongly k-regular if there exist positive integers k, lambda, and mu such that every vertex has k neighbors (i.e., the graph is a ...