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The Kirchhoff index Kf, also simply called the resistance and denoted R (Lukovits et al. 1999), of a connected graph G on n nodes is defined by ...

The digon is the degenerate polygon (corresponding to a line segment) with Schläfli symbol {2}.

The circuit rank gamma, also denoted mu (Volkmann 1996, Babić et al. 2002) or beta (White 2001, p. 56) and known as the cycle rank (e.g., White 2001, p. 56), (first) graph ...

The chromatic number of a graph is at most the maximum vertex degree Delta, unless the graph is complete or an odd cycle, in which case Delta+1 colors are required.

A knot K embedded in R^3=C_z×R_t, where the three-dimensional space R^3 is represented as a direct product of a complex line C with coordinate z and a real line R with ...

Consider a finite collection of points p=(p_1,...,p_n), p_i in R^d Euclidean space (known as a configuration) and a graph G whose graph vertices correspond to pairs of points ...

A graph is a forbidden subgraph if its presence as a subgraph of a given graph means it is not a member of some family of graphs. For example, a bipartite graph is a graph ...

A graph is a forbidden topological minor (also known as a forbidden homeomorphic subgraph) if its presence as a homeomorphic subgraph of a given graph (i.e., there is an ...

The vertex set of a graph is simply a set of all vertices of the graph. The cardinality of the vertex set for a given graph g is known as the vertex count of g. The vertex ...

The algebraic connectivity of a graph is the numerically second smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of a graph G. In other ...