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A framework is called "just rigid" if it is rigid, but ceases to be so when any single bar is removed. Lamb (1928, pp. 93-94) proved that a necessary (but not sufficient) ...

The König-Egeváry theorem, sometimes simply called König's theorem, asserts that the matching number (i.e., size of a maximum independent edge set) is equal to the vertex ...

The Laplacian spectral radius of a finite graph is defined as the largest value of its Laplacian spectrum, i.e., the largest eigenvalue of the Laplacian matrix (Lin et al. ...

A maximal independent set is an independent set which is a maximal set, i.e., an independent set that is not a subset of any other independent set. The generic term "maximal ...

A maximum spanning tree is a spanning tree of a weighted graph having maximum weight. It can be computed by negating the weights for each edge and applying Kruskal's ...

Let G=(V,E) be a (not necessarily simple) undirected edge-weighted graph with nonnegative weights. A cut C of G is any nontrivial subset of V, and the weight of the cut is ...

A minimum clique covering is a clique covering of minimum size, and the size of such a minimum clique covering is known as the clique covering number. Note that while a ...

The network flow problem considers a graph G with a set of sources S and sinks T and for which each edge has an assigned capacity (weight), and then asks to find the maximum ...

A Pareto plot is type of plot used in quality control applications that combines a bar chart displaying percentages of categories in the data with a line graph showing ...

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 ...