The concept of geometric-arithmetic indices was introduced in the chemical graph theory. These indices are defined by the following general formula:     ( ) 2 ( ) uv E G u v u v Q Q Q Q GA G , where Qu is some quantity that in a unique manner can be associated with the vertex u of graph G. In this paper the exact formula for two types of geometric-arithmetic index of Vphenylenic nanotube ar...

We will try to sketch Professor F. Y. Wu's contributions in lattice statistical mechanics, solid state physics, graph theory, enumerative com-binatorics and so many other domains of physics and mathematics. We will recall F. Y. Wu's most important and well-known classic results and we will also sketch his most recent researches dedicated to the connections of lattice statistical mechanical mode...

Young tableaux are ubiquitous combinatorial objects making important and inspiring appearances in representation theory, geometry and algebra. They naturally arise in the study of symmetric functions, representation theory of the symmetric and complex general linear groups, and Schubert calculus of Grassmannians. Discovering and interpreting enumerative formulas for Young tableaux (and their ge...

Abstract Number theory abounds with conjectures asserting that every natural number has some arithmetic property. An example is Goldbach’s Conjecture, which states even greater than 2 the sum of two primes. Enumerative inductive evidence for such usually consists small cases. In absence supporting reasons, mathematicians mistrust arithmetical generalisations, more so most other forms non-deduct...

Algebraic and enumerative combinatorics is concerned with objects that have both a combinatorial and an algebraic interpretation. It is a highly active area of the mathematical sciences, with many connections and applications to other areas, including algebraic geometry, representation theory, topology, mathematical physics and statistical mechanics. Enumerative questions arise in the mathemati...

The method of switchings is a standard tool for enumerative and probabilistic applications in combinatorics. In its simplest form, it analyses a relation between two sets to estimate the ratio of their sizes. In a more complicated setting, there is a family of sets connected by some relations. By bounding properties of the relations, bounds can be inferred on the relative sizes of the sets. In ...

The notion of strong arcs in a fuzzy graph was introduced byBhutani and Rosenfeld in [1] and fuzzy end nodes in the subsequent paper[2] using the concept of strong arcs. In Mordeson and Yao [7], the notion of“degrees” for concepts fuzzified from graph theory were defined and studied.In this note, we discuss degrees for fuzzy end nodes and study further someproperties of fuzzy end nodes and fuzz...

Weconsider the 1D skiving stock problem (SSP)which is strongly related to the dual bin packing problem: find the maximum number of products with minimum length L that can be constructed by connecting a given supply of m ∈ N smaller item lengths l1, . . . , lm with availabilities b1, . . . , bm . For this NP-hard optimization problem, we focus on the proper relaxation and introduce a modeling ap...