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The eigenvector corresponding to the second smallest eigenvalue (i.e., the algebraic connectivity) of the Laplacian matrix of a graph G. The Fiedler vector is used in ...

The group C_2×C_2×C_2 is one of the three Abelian groups of order 8 (the other two groups are non-Abelian). An example is the modulo multiplication group M_(24) (which is the ...

Let (Omega)_(ij) be the resistance distance matrix of a connected graph G on n nodes. Then Foster's theorems state that sum_((i,j) in E(G)))Omega_(ij)=n-1, where E(g) is the ...

Let (x_1,x_2) and (y_1,y_2) be two sets of complex numbers linearly independent over the rationals. Then the four exponential conjecture posits that at least one of ...

French curves are plastic (or wooden) templates having an edge composed of several different curves. French curves are used in drafting (or were before computer-aided design) ...

Consider Kimberling centers X_(20) (de Longchamps point Z; intersection L_S intersection L_E of the Soddy line and Euler line), X_(468) (intersection L_E intersection L_O of ...

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. ...

The girth of a graphs is the length of one of its (if any) shortest graph cycles. Acyclic graphs are considered to have infinite girth (Skiena 1990, p. 191). The girth of a ...

If A is a graded module and there exists a degree-preserving linear map phi:A tensor A->A, then (A,phi) is called a graded algebra. Cohomology is a graded algebra. In ...

The circumference of a graph is the length of any longest cycle in a graph. Hamiltonian graphs on n>1 vertices therefore have circumference of n. For a cyclic graph, the ...