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The minimum vertex degree, sometimes simply called the minimum degree, of a graph G is the smallest vertex degree of G, denoted delta.

The neighborhood complex N(G) of a locally finite graph G is defined as the abstract simplicial complex formed by the subsets of the neighborhoods of all vertices of G.

The term "polyedge" has been variously proposed to refer to a polystick or a simple connected graph on n edges (Muñiz 2011), the latter of which has also been termed an ...

The coloring red of two complete subgraphs of n/2 points (for even n) in order to generate a blue-empty graph.

The shortest path problem seeks to find the shortest path (a.k.a. graph geodesic) connecting two specific vertices (u,v) of a directed or undirected graph. The length of the ...

The nth-order Sierpiński tetrahedron graph is the connectivity graph of black triangles in the nth iteration of the tetrix fractal. The first three iterations are shown ...

Let a cotree of a spanning tree T in a connected graph G be denoted T^*. Then the edges of G which are not in T^* are called its twigs (Harary 1994, p. 39).

A k-factor of a graph is a k-regular subgraph of order n. k-factors are a generalization of complete matchings. A perfect matching is a 1-factor (Skiena 1990, p. 244).

An algebraic ring which appears in treatments of duality in algebraic geometry. Let A be a local Artinian ring with m subset A its maximal ideal. Then A is a Gorenstein ring ...

Percolation, the fundamental notion at the heart of percolation theory, is a difficult idea to define precisely though it is quite easy to describe qualitatively. From the ...