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A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general ...

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 ...

An operator defined on a set S which takes two elements from S as inputs and returns a single element of S. Binary operators are called compositions by Rosenfeld (1968). Sets ...

The symbol intersection , used for the intersection of sets, and sometimes also for the logical connective AND instead of the symbol ^ (wedge). In fact, for any two sets A ...

Let A^~, B^~, ... be operators. Then the commutator of A^~ and B^~ is defined as [A^~,B^~]=A^~B^~-B^~A^~. (1) Let a, b, ... be constants, then identities include [f(x),x] = 0 ...

The symbol union , used for the union of sets, and, sometimes, also for the logical connective OR instead of the symbol v (vee). In fact, for any two sets A and B x in A ...

Let (q_1,...,q_n,p_1,...,p_n) be any functions of two variables (u,v). Then the expression ...

A rational function P(x)/Q(x) can be rewritten using what is known as partial fraction decomposition. This procedure often allows integration to be performed on each term ...

Let u and v be any functions of a set of variables (q_1,...,q_n,p_1,...,p_n). Then the expression ...

There are several definitions of "almost Hamiltonian" in use. As defined by Punnim et al. (2007), an almost Hamiltonian graph is a graph on n nodes having Hamiltonian number ...