Search Results for ""

Let s_k be the number of independent vertex sets of cardinality k in a graph G. The polynomial I(x)=sum_(k=0)^(alpha(G))s_kx^k, (1) where alpha(G) is the independence number, ...

There are several related theorems involving Hamiltonian cycles of graphs that are associated with Pósa. Let G be a simple graph with n graph vertices. 1. If, for every k in ...

A subgraph G^' of a graph G is a graph G^' whose vertex set and edge set are subsets of those of G. If G^' is a subgraph of G, then G is said to be a supergraph of G^' ...

A maximal independent vertex set of a graph is an independent vertex set that cannot be expanded to another independent vertex set by addition of any vertex in the graph. A ...

Define a pebbling move as a transer of two pebbles from one vertex of a graph edge to an adjacent vertex with one of the pebbles being removed in transit as a toll. The ...

There are a number of graphs associated with J. H. Conway. The first is the unique rank-3 strongly regular graph with parameters (nu,k,lambda,mu)=(1408,567,246,216) with ...

A walk is a sequence v_0, e_1, v_1, ..., v_k of graph vertices v_i and graph edges e_i such that for 1<=i<=k, the edge e_i has endpoints v_(i-1) and v_i (West 2000, p. 20). ...

A cubic curve invented by Diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name "cissoid" first appears in the work of ...

An ambiguous figure in which the brain switches between seeing a rabbit and a duck. The duck-rabbit was "originally noted" by American psychologist Joseph Jastrow (Jastrow ...

De Grey (2018) found the first examples of unit-distance graphs with chromatic number 5, thus demonstrating that the solution to the Hadwiger-Nelson problem (i.e., the ...