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Let a graph G have exactly 2n-3 graph edges, where n is the number of graph vertices in G. Then G is "generically" rigid in R^2 iff e^'<=2n^'-3 for every subgraph of G having ...

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

The Laplacian polynomial is the characteristic polynomial of the Laplacian matrix. The second smallest root of the Laplacian polynomial of a graph g (counting multiple values ...

The number of graph edges meeting at a given node in a graph is called the order of that graph vertex.

A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique ...

The local clustering coefficient of a vertex v_i of a graph G is the fraction of pairs of neighbors of v_i that are connected over all pairs of neighbors of v_i. Computation ...

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 (upper) vertex independence number of a graph, often called simply "the" independence number, is the cardinality of the largest independent vertex set, i.e., the size of ...

In a network with three graph edges at each graph vertex, the number of Hamiltonian cycles through a specified graph edge is 0 or even.

A tree is a mathematical structure that can be viewed as either a graph or as a data structure. The two views are equivalent, since a tree data structure contains not only a ...