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Let c_k be the number of vertex covers of a graph G of size k. Then the vertex cover polynomial Psi_G(x) is defined by Psi_G(x)=sum_(k=0)^(|G|)c_kx^k, (1) where |G| is the ...

LCF notation is a concise and convenient notation devised by Joshua Lederberg (winner of the 1958 Nobel Prize in Physiology and Medicine) for the representation of cubic ...

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, ...

The Morgan-Voyce polynomials are polynomials related to the Brahmagupta and Fibonacci polynomials. They are defined by the recurrence relations b_n(x) = ...

Given an open subset U in n-dimensional space and two compact subsets C_0 and C_1 of U, where C_1 is derived from C_0 by a continuous motion, is it possible to move C_0 to ...

Let G be an undirected graph, and let i denote the cardinal number of the set of externally active edges of a spanning tree T of G, j denote the cardinal number of the set of ...

The Knödel graph W_(Delta,n) is a regular bipartite graph of vertex degree Delta on n nodes for even n>=2 and 1<=Delta<=|_log_2n_| with edges defined as follows. Label the ...

The bipartite double graph, also called the Kronecker cover, Kronecker double cover, bipartite double cover, canonical double cover, or bipartite double, of a given graph G ...

The domino graph is the graph on 6 vertices illustrated above. It is isomorphic to the 3-ladder graph and the (2,3)-grid graph. It is implemented in the Wolfram Language as ...

The likelihood of a simple graph is defined by starting with the set S_1={(K_11)}. The following procedure is then iterated to produce a set of graphs G_n of order n. At step ...