Convex 3-polytopes with exactly two types of edges
Abstract We consider convex 3-polytopes with exactly two types of edges. The questions of the existence of such 3-polytopes are solved. The cardinalities of all classes are determined.
Pentagonal 3-polytopal graphs with edges of only two types and shortness parameters
We consider the class of pentagonal 3-polytopal graphs all of whose edges are incident either with two 3-valent vertices or with a 3-valent vertex and a q-valent vertex. For most values of q, (i) we find a small non-hamiltonian graph in the class and (ii) we show that the shortness exponent of the class and the shortness coefficient of a special subclass are less than one. For q=4, we find a positive lower bound for the shortness coefficient.
Representations and computations of {2, 3~} and {2, 4~}-inverses in indefinite inner product spaces
We investigate full-rank representations of { 2 , 3 ~ } and { 2 , 4 ~ } -inverses with prescribed rank as well as with prescribed range and null space in an indefinite inner product space. In certain particular cases we obtain new results or generalizations related with { 2 , 3 } and { 2 , 4 } -inverses in a Hilbert (unitary) space. Direct and iterative methods for computing { 2 , 3 ~ } and { 2 , 4 ~ } -inverses in an indefinite inner product space are developed. Numerical examples with different metric matrices are presented.