We present new functional equations connecting the counting series of plane and planar (in the sense of Harary and Palmer) dissections. Simple rigorous expressions for counting symmetric r-dissections of polygons and planar S-dissections are obtained.

In this paper we will investigate the edge-chromatic automorphism groups for two classes of graphs. Chromatic automorphism groups have been studied by a number of people, including Chvatal [4] and Baumann et al. [l, 21. Characterizations will be given for these groups. Note that all arithmetic will be done modp, p not necessarily prime. The particular p will be clear from the context. These gra...

We show that the local period at position n in a characteristic Sturmian word can be given in terms of the Ostrowski representation for n+ 1.

Motivated by the work of George A. Anastassiou in [George A. Anastassiou, Ostrowski and Landau inequalities for Banach space valued functions, Mathematical and Computer Modelling, 55 (2012), 312–329], we derive some Landau type inequalities for Banach space valued functions without assuming the boundary conditions.

Here we define a Caputo like discrete nabla fractional difference and we produce discrete nabla fractional Taylor formulae for the first time. We estimate their remaiders. Then we derive related discrete nabla fractional Opial, Ostrowski, Poincaré and Sobolev type inequalities .

We present optimal upper bounds for the deviation of a fuzzy continuous function from its fuzzy average over [a, b] ⊂ R, error is measured in the D-fuzzy metric. The established fuzzy Ostrowski type inequalities are sharp, in fact attained by simple fuzzy real number valued functions. These inequalities are given for fuzzy Hölder and fuzzy differentiable functions and these facts are reflected ...

This paper deals with two types of graph labelings namely, the super (a, d)-edge antimagic total labeling and super (a, d)-vertex antimagic total labeling on the Harary graph C n. We also construct the super edge-antimagic and super vertex-antimagic total labelings for a disjoint union of k identical copies of the Harary graph.

A graph is said to be a sum graph if there exists a set S of positive integers as its node set, with two nodes adjacent whenever their sum is in S. An integral sum graph is defined just as the sum graph, the difference being that S is a subset of 2~ instead of N*. The sum number of a given graph G is defined as the smallest number of isolated nodes which when added to G result in a sum graph. T...