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Given a complete graph K_n which is two-colored, the number of forced monochromatic triangles is at least {1/3u(u-1)(u-2) for n=2u; 2/3u(u-1)(4u+1) for n=4u+1; ...

In general, a topological index, sometimes also known as a graph-theoretic index, is a numerical invariant of a chemical graph (Plavšić et al. 1993). Particular topological ...

An AB percolation is a discrete percolation model in which the underlying point lattice graph L has the properties that each of its graph vertices is occupied by an atom ...

The cotree T^* of a spanning tree T in a connected graph G is the spacing subgraph of G containing exactly those edges of G which are not in T (Harary 1994, p. 39).

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).

The set E of edges of a loopless graph (V,E), being a set of unordered pairs of elements of V, constitutes an adjacency relation on V. Formally, an adjacency relation is any ...

The term "snark" was first popularized by Gardner (1976) as a class of minimal cubic graphs with edge chromatic number 4 and certain connectivity requirements. (By Vizing's ...

Suppose that G is a pseudograph, E is the edge set of G, and C is the family of edge sets of graph cycles of G. Then C obeys the axioms for the circuits of a matroid, and ...

In the directed graph above, pick any vertex and follow the arrows in sequence blue-red-red three times. You will finish at the green vertex. Similarly, follow the sequence ...

The Laplacian matrix, sometimes also called the admittance matrix (Cvetković et al. 1998, Babić et al. 2002) or Kirchhoff matrix, of a graph G, where G=(V,E) is an ...