On Cayley's enumeration of alkanes (or 4-valent trees).
On Cayley's formula for counting trees in nested interval graphs.
On CCC boolean algebras and partial orders
We partially strengthen a result of Shelah from [Sh] by proving that if and is a CCC partial order with e.g. (the successor of ) and then is -linked.
On centrally symmetric graphs
In this note we extend results on the covering graphs of modular lattices (Zelinka) and semimodular lattices (Gedeonova, Duffus and Rival) to the covering graph of certain graded lattices.
On Certain Classes of rigid groups
On certain combinatorial identities
On Certain Edge-Critical Graphs of a Given Diameter
On certain eigenspaces of cographs.
On certain extensions of intervals in graphs
On certain formulas of Karlin and Szegö.
On certain generalized q-Appell polynomial expansions
We study q-analogues of three Appell polynomials, the H-polynomials, the Apostol-Bernoulli and Apostol-Euler polynomials, whereby two new q-difference operators and the NOVA q-addition play key roles. The definitions of the new polynomials are by the generating function; like in our book, two forms, NWA and JHC are always given together with tables, symmetry relations and recurrence formulas. It is shown that the complementary argument theorems can be extended to the new polynomials as well as to...
On Certain Homomorphism Properties of Graphs I.
On certain integral Schreier graphs of the symmetric group.
On certain n-connected matroids.
On certain regular graphs of girth 5.
On character tables related to the alternating groups.
On characterization of uniquely 3-list colorable complete multipartite graphs
For each vertex v of a graph G, if there exists a list of k colors, L(v), such that there is a unique proper coloring for G from this collection of lists, then G is called a uniquely k-list colorable graph. Ghebleh and Mahmoodian characterized uniquely 3-list colorable complete multipartite graphs except for nine graphs: r ∈ 4,5,6,7,8, , , , . Also, they conjectured that the nine graphs are not U3LC graphs. After that, except for r ∈ 4,5,6,7,8, the others have been proved not to be U3LC...
On Chebyshev's polynomials and certain combinatorial identities.
On Cherednik-Macdonald-Mehta identities.
On chirality groups and regular coverings of regular oriented hypermaps
We prove that if the Walsh bipartite map of a regular oriented hypermap is also orientably regular then both and have the same chirality group, the covering core of (the smallest regular map covering ) is the Walsh bipartite map of the covering core of and the closure cover of (the greatest regular map covered by ) is the Walsh bipartite map of the closure cover of . We apply these results to the family of toroidal chiral hypermaps induced by the family of toroidal bipartite maps...