Polynomial sequences pn(x) of binomial type are a principal tool in the umbral calculus of enumerative combinatorics. We express pn(x) as a path integral in the “phase space” N× [−π, π]. The Hamiltonian is h(φ) = ∑n=0 p ′ n(0)/n!e inφ and it produces a Schrödinger type equation for pn(x). This establishes a bridge between enumerative combinatorics and quantum field theory. It also provides an a...

The cyclic ladder graph CLn is the Cartesian product of cycles Cn and paths P2, that CLn=Cn×P2, (n≥3). di-forcing polynomial a binary enumerative all perfect matching forcing anti-forcing numbers. In this paper, we derive recursive formulas for by classifying counting cases associated edges given vertex, from which obtain number matching, polynomials, generating function computing some polynomi...

Graph theory based methods are powerful means for representing structural systems so that their geometry and topology can be understood clearly. The combination of graph theory based methods and some metaheuristics can offer effective solutions for complex engineering optimization problems. This paper presents a Charged System Search (CSS) algorithm for the free shape optimizations of thin-wall...

the first geometric-arithmetic index was introduced in the chemical theory as the summationof 2 du dv /(du  dv ) overall edges of the graph, where du stand for the degree of the vertexu. in this paper we give the expressions for computing the first geometric-arithmetic index ofhexagonal systems and phenylenes and present new method for describing hexagonal systemby corresponding a simple graph...

let $g$ be a non-abelian group and let $z(g)$ be the center of $g$. associate with $g$ there is agraph $gamma_g$ as follows: take $gsetminus z(g)$ as vertices of$gamma_g$ and joint two distinct vertices $x$ and $y$ whenever$yxneq yx$. $gamma_g$ is called the non-commuting graph of $g$. in recent years many interesting works have been done in non-commutative graph of groups. computing the clique...

abstract: in this study an appropriate computational approach was presented for estimating the boiling temperatures of 41 different types of olefins and their derivatives. based on the guidelines of this approach, several structural indices related to the organic components were applied using graph theory. meanwhile, in addition to evaluating the relation between the boiling temperatures of ole...