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Every semisimple Lie algebra g is classified by its Dynkin diagram. A Dynkin diagram is a graph with a few different kinds of possible edges. The connected components of the ...

Two nonisomorphic graphs that have equal resistance spectra (i.e., multisets of resistance distances) are said to be resistance-equivalent. All nonisomorphic simple graphs on ...

In complex analysis, a branch (also called a sheet) is a portion of the range of a multivalued function over which the function is single-valued. Combining all the sheets ...

A random-connection model (RCM) is a graph-theoretic model of continuum percolation theory characterized by the existence of a stationary point process X and a non-increasing ...

Tracing through the connections of a branchial graph gives rise to the notion of a kind of space in which states on different branches of history are laid out. In particular, ...

In plane geometry, a chord is the line segment joining two points on a curve. The term is often used to describe a line segment whose ends lie on a circle. The term is also ...

The tetragonal trapezohedron is the dual of the square antiprism. For a square antiprism with unit edge lengths, the edge lengths of the corresponding tetragonal ...

The Steiner tree of some subset of the vertices of a graph G is a minimum-weight connected subgraph of G that includes all the vertices. It is always a tree. Steiner trees ...

The pentakis icosidodecahedron is the dual of the chamfered dodecahedron. It contains 42 vertices, 120 edges, and 80 faces. The canonical version has two distinct edge ...

The equilateral triaugmented triangular prism is the Johnson solid J_(51) constructed by erecting a regular tetrahedron on each square face of an equilateral triangular ...