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The Randić matrix A_(Randic) of a simple graph is a weighted adjacency matrix with weight f(d_i,d_j)=1/(sqrt(d_id_j)), (1) where d_i are the vertex degrees of the graph. In ...

The total domination number gamma_t of a graph is the size of a smallest total dominating set, where a total dominating set is a set of vertices of the graph such that all ...

A biplanar graph is defined as a graph that is the graph union of two planar edge-induced subgraphs. In other words, biplanar graphs are graphs with graph thickness 1 or 2 ...

The line R[s]=1/2 in the complex plane on which the Riemann hypothesis asserts that all nontrivial (complex) Riemann zeta function zeros lie. The plot above shows the first ...

Form a sequence from an alphabet of letters [1,n] such that there are no consecutive letters and no alternating subsequences of length greater than d. Then the sequence is a ...

A lucky number of Euler is a number p such that the prime-generating polynomial n^2-n+p is prime for n=1, 2, ..., p-1. Such numbers are related to the imaginary quadratic ...

Let K_1 be a knot inside a torus, and knot the torus in the shape of a second knot (called the companion knot) K_2, with certain additional mild restrictions to avoid trivial ...

A number of the form aba..., abab..., etc. The first few nontrivial undulants (with the stipulation that a!=b) are 101, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, ... ...

An apex graph is a graph possessing at least one vertex whose removal results in a planar graph. The set of vertices whose removal results in a planar graph is known as the ...

If replacing each number by its square in a magic square produces another magic square, the square is said to be a bimagic square. Bimagic squares are also called doubly ...