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An interpretation of first-order logic consists of a non-empty domain D and mappings for function and predicate symbols. Every n-place function symbol is mapped to a function ...

A graph G=(V,E) is an interval graph if it captures the intersection relation for some set of intervals on the real line. Formally, P is an interval graph provided that one ...

The concept of irredundance was introduced by Cockayne et al. (1978). Let N_G[v] denote the graph neighborhood of a vertex v in a graph G (including v itself), and let N_G[S] ...

In general, it is possible to link two n-dimensional hyperspheres in (n+2)-dimensional space in an infinite number of inequivalent ways. In dimensions greater than n+2 in the ...

Every nonplanar graph contains either the utility graph K_(3,3) (i.e., the complete bipartite graph on two sets of three vertices) or the pentatope graph K_5 as a ...

Lagrange's identity is the algebraic identity (sum_(k=1)^na_kb_k)^2=(sum_(k=1)^na_k^2)(sum_(k=1)^nb_k^2)-sum_(1<=k<j<=n)(a_kb_j-a_jb_k)^2 (1) (Mitrinović 1970, p. 41; Marsden ...

A Lyapunov function is a scalar function V(y) defined on a region D that is continuous, positive definite, V(y)>0 for all y!=0), and has continuous first-order partial ...

A Markov chain is collection of random variables {X_t} (where the index t runs through 0, 1, ...) having the property that, given the present, the future is conditionally ...

The (upper) matching number nu(G) of graph G, sometimes known as the edge independence number, is the size of a maximum independent edge set. Equivalently, it is the degree ...

The minimal polynomial of a matrix A is the monic polynomial in A of smallest degree n such that p(A)=sum_(i=0)^nc_iA^i=0. (1) The minimal polynomial divides any polynomial q ...