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A maximal clique is a clique that cannot be extended by including one more adjacent vertex, meaning it is not a subset of a larger clique. A maximum clique (i.e., clique of ...

The graph corresponding to the complete k-ary tree on n nodes is implemented in the Wolfram Language as KaryTree[n, k].

By analogy with the divisor function sigma_1(n), let pi(n)=product_(d|n)d (1) denote the product of the divisors d of n (including n itself). For n=1, 2, ..., the first few ...

If x_0 is an ordinary point of the ordinary differential equation, expand y in a Taylor series about x_0. Commonly, the expansion point can be taken as x_0=0, resulting in ...

Let P be a finite partially ordered set, then an antichain in P is a set of pairwise incomparable elements. Antichains are also called Sperner systems in older literature ...

The average disorder number of a simple connected graph on n vertices is defined as the average length of a walk along the edges of the graph taken over all ordering of its ...

A k-matching in a graph G is a set of k edges, no two of which have a vertex in common (i.e., an independent edge set of size k). Let Phi_k be the number of k-matchings in ...

Let gamma(G) denote the domination number of a simple graph G. Then Vizing (1963) conjectured that gamma(G)gamma(H)<=gamma(G×H), where G×H is the graph product. While the ...

"Neighborhood" is a word with many different levels of meaning in mathematics. One of the most general concepts of a neighborhood of a point x in R^n (also called an ...

A modulo multiplication group is a finite group M_m of residue classes prime to m under multiplication mod m. M_m is Abelian of group order phi(m), where phi(m) is the ...