Some geometric probability problems involving the Eulerian numbers.
Some globally determined classes of graphs
For a class of graphs we say that it is globally determined if any two nonisomorphic graphs from that class have nonisomorphic globals. We will prove that the class of so called CCB graphs and the class of finite forests are globally determined.
Some graphic uses of an even number of odd nodes
Vertex-degree parity in large implicit “exchange graphs” implies some EP theorems asserting the existence of a second object without evidently providing a polytime algorithm for finding a second object.
Some graphs determined by their (signless) Laplacian spectra
Let be the wheel graph on vertices, and let be the graph on vertices obtained by attaching pendant edges together with hanging paths of length two at vertex , where is the unique common vertex of triangles. In this paper we show that (, ) and are determined by their signless Laplacian spectra, respectively. Moreover, we also prove that and its complement graph are determined by their Laplacian spectra, respectively, for and .
Some graphs with extremal Szeged index
Some gregarious cycle decompositions of complete equipartite graphs.
Some hardness results for question/answer games.
Some Heuristics in Automatic Theorem Proving
Some heuristics in automatic theorem proving.
Some identities for Chebyshev polynomials.
Some identities for factorials and binomial coefficients
Some inequalities for Kurepa's functions.
Some inequalities in functional analysis, combinatorics, and probability theory.
Some infinite p-groups.
Some interesting series arising from the power series expansion of .
Some interpretations of the -Fibonacci numbers
In this paper we consider two parameters generalization of the Fibonacci numbers and Pell numbers, named as the -Fibonacci numbers. We give some new interpretations of these numbers. Moreover using these interpretations we prove some identities for the -Fibonacci numbers.
Some maximum multigraphs and edge/vertex distance colourings
Shannon-Vizing-type problems concerning the upper bound for a distance chromatic index of multigraphs G in terms of the maximum degree Δ(G) are studied. Conjectures generalizing those related to the strong chromatic index are presented. The chromatic d-index and chromatic d-number of paths, cycles, trees and some hypercubes are determined. Among hypercubes, however, the exact order of their growth is found.
Some new classes of graceful Lobsters obtained from diameter four trees
We observe that a lobster with diameter at least five has a unique path with the property that besides the adjacencies in both and are adjacent to the centers of at least one , where , and each , , is adjacent at most to the centers of some , where . This path is called the central path of the lobster. We call an even branch if is nonzero even, an odd branch if is odd and a pendant branch if . In the existing literature only some specific classes of lobsters have been found...
Some new exact van der Waerden numbers.
Some new facts about group 𝒢 generated by the family of convergent permutations
The aim of this paper is to present some new and essential facts about group 𝒢 generated by the family of convergent permutations, i.e. the permutations on ℕ preserving the convergence of series of real terms. We prove that there exist permutations preserving the sum of series which do not belong to 𝒢. Additionally, we show that there exists a family G (possessing the cardinality equal to continuum) of groups of permutations on ℕ such that each one of these groups is different than 𝒢 and is composed...