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The rank polynomial R(x,y) of a general graph G is the function defined by R(x,y)=sum_(S subset= E(G))x^(r(S))y^(s(S)), (1) where the sum is taken over all subgraphs (i.e., ...

A (general) octahedron is a polyhedron having eight faces. Examples include the 4-trapezohedron, augmented triangular prism (Johnson solid J_(49)), bislit cube, Dürer solid, ...

The connected domination number of a connected graph G, denoted d(G), is the size of a minimum connected dominating set of a graph G. The maximum leaf number l(G) and ...

The augmented tridiminished icosahedron is Johnson solid J_(64), which is formed from augmentation of the triangular face adjecent to all three hexagons of the tridiminished ...

Baxter's four-coloring constant for a triangular lattice is given by C^2 = product_(j=1)^(infty)((3j-1)^2)/((3j-2)(3j)) (1) = 3/(4pi^2)Gamma^3(1/3) (2) = 1.46099848... (3) ...

The maximum leaf number l(G) of a graph G is the largest number of tree leaves in any of its spanning trees. (The corresponding smallest number of leaves is known as the ...

The mathematical study of the properties of the formal mathematical structures called graphs.

The multiplicity of a multigraph is its maximum edge multiplicity.

A labeling phi of (the vertices) of a graph G with positive integers taken from the set {1,2,...,r} is said to be r-distinguishing if no graph automorphism of G preserves all ...

Newton's method for finding roots of a complex polynomial f entails iterating the function z-[f(z)/f^'(z)], which can be viewed as applying the Euler backward method with ...