We study the family of closed Riemannian n-manifolds with holonomy group isomorphic to Z2n-1, which we call generalized Hantzsche-Wendt manifolds. We prove results on their structure, compute some invariants, and find relations between them, illustrated in a graph connecting the family.
We obtain upper bounds for generalized indices of matrices in the class of nearly reducible Boolean matrices and in the class of critically reducible Boolean matrices, and prove that these bounds are the best possible.
We prove: (1) that can be arbitrarily large, where and are P-choice and P-chromatic numbers, respectively, (2) the (P,L)-colouring version of Brooks’ and Gallai’s theorems.
For natural numbers k and n, where 2 ≤ k ≤ n, the vertices of a graph are labeled using the elements of the k-fold Cartesian product Iₙ × Iₙ × ... × Iₙ. Two particular graph constructions will be given and the graphs so constructed are called generalized matrix graphs. Properties of generalized matrix graphs are determined and their application to completely independent critical cliques is investigated. It is shown that there exists a vertex critical graph which admits a family of k completely independent...
We define the generalized outerplanar index of a graph and give a full characterization of graphs with respect to this index.
We give a generalization of poly-Cauchy polynomials and investigate their arithmetical and combinatorial properties. We also study the zeta functions which interpolate the generalized poly-Cauchy polynomials.
In this paper we translate Ramsey-type problems into the language of decomposable hereditary properties of graphs. We prove a distributive law for reducible and decomposable properties of graphs. Using it we establish some values of graph theoretical invariants of decomposable properties and show their correspondence to generalized Ramsey numbers.
We introduce a new family of generalized Schröder matrices from the Riordan arrays which are obtained by counting of the weighted lattice paths with steps , , , and and not going above the line . We also consider the half of the generalized Delannoy matrix which is derived from the enumeration of these lattice paths with no restrictions. Correlations between these matrices are considered. By way of illustration, we give several examples of Riordan arrays of combinatorial interest. In addition,...