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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 Randić spectral radius rho_(Randic) of a graph is defined as the largest eigenvalue of its Randić matrix.

If the rank polynomial R(x,y) of a graph G is given by sumrho_(rs)x^ry^s, then rho_(rs) is the number of subgraphs of G with rank r and co-rank s, and the matrix (rho_(rs)) ...

The so-called reaching algorithm can solve the shortest path problem (i.e., the problem of finding the graph geodesic between two given nodes) on an m-edge graph in O(m) ...

The number of ways N(m,n) of finding a subrectangle with an m×n rectangle can be computed by counting the number of ways in which the upper right-hand corner can be selected ...

Let a sequence be defined by A_(-1) = s (1) A_0 = 3 (2) A_1 = r (3) A_n = rA_(n-1)-sA_(n-2)+A_(n-3). (4) Also define the associated polynomial f(x)=x^3-rx^2+sx+1, (5) and let ...

A method of proof which proceeds by stating a proposition and then showing that it results in a contradiction, thus demonstrating the proposition to be false. In the words of ...

A system in which words (expressions) of a formal language can be transformed according to a finite set of rewrite rules is called a reduction system. While reduction systems ...

Regular expressions define formal languages as sets of strings over a finite alphabet. Let sigma denote a selected alphabet. Then emptyset is a regular expression that ...

Consider a two-dimensional tessellation with q regular p-gons at each polygon vertex. In the plane, (1-2/p)pi=(2pi)/q (1) 1/p+1/q=1/2, (2) so (p-2)(q-2)=4 (3) (Ball and ...