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A finite simple connected graph G is quadratically embeddable if its quadratic embedding constant QEC(G) is nonpositive, i.e., QEC(G)<=0. A graph being quadratically ...

The term in rigidity theory for the edges of a graph.

The complement of a graph G, sometimes called the edge-complement (Gross and Yellen 2006, p. 86), is the graph G^', sometimes denoted G^_ or G^c (e.g., Clark and Entringer ...

The graph complement of a graph hole. Graph antiholes are called even if they have an even number of vertices and odd if they have an odd number of vertices (Chvátal). No odd ...

A web diagram, also called a cobweb plot, is a graph that can be used to visualize successive iterations of a function y=f(x). In particular, the segments of the diagram ...

A Taylor graph is a distance-regular graph with intersection array {k,mu,1;1,mu,k}. A Taylor graph with these parameters has 2(k+1) vertices. The crown graphs K_2 square ...

Lovász (1970) conjectured that every connected vertex-transitive graph is traceable (Gould, p. 33). This conjecture was subsequently verified for several special orders and ...

Let V(G) be the vertex set of a simple graph and E(G) its edge set. Then a graph isomorphism from a simple graph G to a simple graph H is a bijection f:V(G)->V(H) such that ...

For a graph vertex x of a graph, let Gamma_x and Delta_x denote the subgraphs of Gamma-x induced by the graph vertices adjacent to and nonadjacent to x, respectively. The ...

The circumference of a graph is the length of any longest cycle in a graph. Hamiltonian graphs on n>1 vertices therefore have circumference of n. For a cyclic graph, the ...