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There are several definitions of the strength of a graph. Harary and Palmer (1959) and Harary and Palmer (1973, p. 66) define the strength of a tree as the maximum number of ...

A labeled graph whose nodes are indexed by the generators of a Coxeter group having (P_i,P_j) as an graph edge labeled by M_(ij) whenever M_(ij)>2, where M_(ij) is an element ...

A local sink is a node of a directed graph with no exiting edges, also called a terminal (Borowski and Borwein 1991, p. 401; left figure). A global sink (often simply called ...

There exists no known P algorithm for graph isomorphism testing, although the problem has also not been shown to be NP-complete. In fact, the problem of identifying ...

Seymour conjectured that a graph G of order n with minimum vertex degree delta(G)>=kn/(k+1) contains the kth graph power of a Hamiltonian cycle, generalizing Pósa's ...

An Eulerian cycle, also called an Eulerian circuit, Euler circuit, Eulerian tour, or Euler tour, is a trail which starts and ends at the same graph vertex. In other words, it ...

The center of a graph G is the set of vertices of graph eccentricity equal to the graph radius (i.e., the set of central points). In the above illustration, center nodes are ...

A (p,q)-graph is edge-graceful if the edges can be labeled 1 through q in such a way that the labels induced on the vertices by summing over incident edges modulo p are ...

The Descartes snarks are a set of snarks on 210 vertices and 315 edges discovered by William Tutte in 1948 writing under the pseudonym Blanche Descartes (Descartes 1948; ...

A graph G is fully reconstructible in C^d if the graph is determined from its d-dimensional measurement variety. If G is globally rigid in R^d on n>=d+2 vertices, then G is ...