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Let G be a planar graph whose vertices have been properly colored and suppose v in V(G) is colored C_1. Define the C_1C_2-Kempe chain containing v to be the maximal connected ...

As proposed by Hosoya (1971), the Hosoya index (also called Z-index) of a graph is defined by Z = sum_(k=0)^(n)|a_k| (1) = sum_(k=0)^(n)b_k, (2) where n is the number of ...

An independent vertex set of a graph G is a subset of the vertices such that no two vertices in the subset represent an edge of G. The figure above shows independent sets ...

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 ...

A matchstick graph is a simple graph which has a graph embedding that is planar, for which all distances between vertices have unit distance, and which is non-degenerate (so ...

The Wiener index W, denoted w (Wiener 1947) and also known as the "path number" or Wiener number (Plavšić et al. 1993), is a graph index defined for a graph on n nodes by ...

A cycle of a graph G, also called a circuit if the first vertex is not specified, is a subset of the edge set of G that forms a path such that the first node of the path ...

A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of ...

An antiprism graph is a graph corresponding to the skeleton of an antiprism. Antiprism graphs are therefore polyhedral and planar. The n-antiprism graph has 2n vertices and ...

A cylindrical wedge, also called a cylindrical hoof or cylindrical ungula, is a wedge cut from a cylinder by slicing with a plane that intersects the base of the cylinder. ...