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The ratio of the independence number of a graph G to its vertex count is known as the independence ratio of G (Bollobás 1981). The product of the chromatic number and ...

The number M_2(n) = 1/nsum_(k=1)^(n^2)k (1) = 1/2n(n^2+1) (2) to which the n numbers in any horizontal, vertical, or main diagonal line must sum in a magic square. The first ...

The n-Pasechnik graph is a strongly regular graph on (4n-1)^2 vertices constructed from a skew Hadamard matrix of order 4n. It has regular parameters . The 1-Pasechnik is ...

The treewidth is a measure of the count of original graph vertices mapped onto any tree vertex in an optimal tree decomposition. Determining the treewidth of an arbitrary ...

The algebraic connectivity of a graph is the numerically second smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of a graph G. In other ...

A circular embedding is a graph embedding in which all graph vertices lie on a common circle, usually arranged so they are equally spaced around the circumference. Specific ...

Let S be a set and F={S_1,...,S_p} a nonempty family of distinct nonempty subsets of S whose union is union _(i=1)^pS_i=S. The intersection graph of F is denoted Omega(F) and ...

A doublecross graph is a graph with graph crossing number 2. The numbers of doublecross simple graphs on n=1 nodes are 0, 0, 0, 0, 0, 1, 39, ..., and the numbers of connected ...

Given a distance-regular graph G with integers b_i,c_i,i=0,...,d such that for any two vertices x,y in G at distance i=d(x,y), there are exactly c_i neighbors of y in ...

The arithmetic-geometric energy of a graph is defined as the graph energy of its arithmetic-geometric matrix, i.e., the sum of the absolute values of the eigenvalues of its ...