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A generalized Vandermonde matrix of two sequences a and b where a is an increasing sequence of positive integers and b is an increasing sequence of nonnegative integers of ...

Given a linear code C, a generator matrix G of C is a matrix whose rows generate all the elements of C, i.e., if G=(g_1 g_2 ... g_k)^(T), then every codeword w of C can be ...

A d-dimensional framework is a pair (G,p) where G=(V,E) is a graph with vertex set V and edge set E and p:V->R^d is a map that assigns a point in R^d to each vertex of G. The ...

A number given by the generating function (2t)/(e^t+1)=sum_(n=1)^inftyG_n(t^n)/(n!). (1) It satisfies G_1=1, G_3=G_5=G_7=...=0, and even coefficients are given by G_(2n) = ...

A topologically invariant property of a surface defined as the largest number of nonintersecting simple closed curves that can be drawn on the surface without separating it. ...

Let I(x,y) denote the set of all vertices lying on an (x,y)-graph geodesic in G, then a set S with I(S)=V(G) is called a geodetic set in G and is denoted g(G).

Given a planar graph G, its geometric dual G^* is constructed by placing a vertex in each region of G (including the exterior region) and, if two regions have an edge x in ...

A quantitative measure of the simplicity of a geometric construction which reduces geometric constructions to five steps. It was devised by È. Lemoine. S_1 Place a ...

The Georges graph, illustrated above, is 50-node graph which is the smallest currently known example of a 3-connected bicubic nonhamiltonian graph. It is implemented in the ...

The internal (external) bisecting plane of a dihedral angle of a tetrahedron divides the opposite edge in the ratio of the areas of the adjacent faces.