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The Royle graphs are the two unique simple graphs on eight nodes whose sigma polynomials have nonreal roots (Read and Wilson 1998, p. 265). The sigma polynomials of these ...

The Kirchhoff sum index KfS is a graph index defined for a graph on n nodes by KfS=1/2sum_(i=1)^nsum_(j=1)^n((Omega)_(ij))/((d)_(ij)), where (Omega)_(ij) is the resistance ...

A partition is a way of writing an integer n as a sum of positive integers where the order of the addends is not significant, possibly subject to one or more additional ...

Let B_k be the kth Bernoulli number and consider nB_(n-1)=-1 (mod n), where the residues of fractions are taken in the usual way so as to yield integers, for which the ...

The term "Euler graph" is sometimes used to denote a graph for which all vertices are of even degree (e.g., Seshu and Reed 1961). Note that this definition is different from ...

In general, an extremal graph is the largest graph of order n which does not contain a given graph G as a subgraph (Skiena 1990, p. 143). Turán studied extremal graphs that ...

An untraceable graph is a graph that does not possess a Hamiltonian path, i.e., one that is not traceable. All disconnected graphs are therefore untraceable. Untraceable ...

A cubic number is a figurate number of the form n^3 with n a positive integer. The first few are 1, 8, 27, 64, 125, 216, 343, ... (OEIS A000578). The protagonist Christopher ...

Power formulas include sin^2x = 1/2[1-cos(2x)] (1) sin^3x = 1/4[3sinx-sin(3x)] (2) sin^4x = 1/8[3-4cos(2x)+cos(4x)] (3) and cos^2x = 1/2[1+cos(2x)] (4) cos^3x = ...

An alternating knot is a knot which possesses a knot diagram in which crossings alternate between under- and overpasses. Not all knot diagrams of alternating knots need be ...