scholarly journals The higher-order matching polynomial of a graph

2005 ◽  
Vol 2005 (10) ◽  
pp. 1565-1576 ◽  
Author(s):  
Oswaldo Araujo ◽  
Mario Estrada ◽  
Daniel A. Morales ◽  
Juan Rada
Keyword(s):  
Hypergeometric Functions ◽  
Higher Order ◽  
Disjoint Paths ◽  
Hosoya Index ◽  
Matching Polynomial ◽  
Similarities And Differences

Given a graphGwithnvertices, letp(G,j)denote the number of waysjmutually nonincident edges can be selected inG. The polynomialM(x)=∑j=0[n/2](−1)jp(G,j)xn−2j, called the matching polynomial ofG, is closely related to the Hosoya index introduced in applications in physics and chemistry. In this work we generalize this polynomial by introducing the number of disjoint paths of lengtht, denoted bypt(G,j). We compare this higher-order matching polynomial with the usual one, establishing similarities and differences. Some interesting examples are given. Finally, connections between our generalized matching polynomial and hypergeometric functions are found.

scholarly journals TRANSCENDENCE OF SPECIAL VALUES OF POCHHAMMER FUNCTIONS

2009 ◽  
Vol 05 (04) ◽  
pp. 667-677
Author(s):  
MARVIN D. TRETKOFF ◽  
PAULA TRETKOFF
Keyword(s):  
Hypergeometric Functions ◽  
Higher Order ◽  
Algebraic Numbers ◽  
Special Values

In this paper, we examine the set of algebraic numbers at which higher order hypergeometric functions take algebraic values. In particular, we deduce criteria for this set to be finite and for it to be infinite.

scholarly journals Two Classes of Topological Indices of Phenylene Molecule Graphs

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Tingzeng Wu
Keyword(s):  
Topological Indices ◽  
Extremal Graph ◽  
Hosoya Index ◽  
Matching Polynomial ◽  
Conjugated Hydrocarbons ◽  
Independent Edge ◽  
The Absolute

A phenylene is a conjugated hydrocarbons molecule composed of six- and four-membered rings. The matching energy of a graphGis equal to the sum of the absolute values of the zeros of the matching polynomial ofG, while the Hosoya index is defined as the total number of the independent edge sets ofG. In this paper, we determine the extremal graph with respect to the matching energy and Hosoya index for all phenylene chains.

scholarly journals Maximum Multiplicity of a Root of the Matching Polynomial of a Tree and Minimum Path Cover

10.37236/170 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Cheng Yeaw Ku ◽  
K. B. Wong
Keyword(s):  
Disjoint Paths ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Path Cover ◽  
Minimum Path ◽  
Matching Polynomial ◽  
Minimum Number ◽  
Necessary And Sufficient ◽  
Vertex Disjoint ◽  
Maximum Multiplicity

We give a necessary and sufficient condition for the maximum multiplicity of a root of the matching polynomial of a tree to be equal to the minimum number of vertex disjoint paths needed to cover it.

Matching polynomials for some nanostar dendrimers

2021 ◽  
pp. 2150188
Author(s):  
Fateme movahedi
Keyword(s):  
Hosoya Index ◽  
Matching Polynomial ◽  
Recursive Formulas

Dendrimers are highly branched monodisperse, macromolecules and are considered in nanotechnology with a variety of suitable applications. In this paper, the matching polynomial and some results of the matchings for three classes of nanostar dendrimers are obtained. Furthermore, we express the recursive formulas of the Hosoya index for these structures of dendrimers by their matching polynomials.

scholarly journals Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions

2020 ◽  
Author(s):  
Feng Qi ◽  
Chuan-Jun Huang
Keyword(s):  
Hypergeometric Function ◽  
General Formula ◽  
Differentiable Function ◽  
Inversion Formula ◽  
Hypergeometric Functions ◽  
Beta Function ◽  
Higher Order ◽  
Gauss Hypergeometric Function ◽  
Partial Derivatives ◽  
Real Academia

In the paper, by virtue of the binomial inversion formula, a general formula of higher order derivatives for a ratio of two differentiable function, and other techniques, the authors compute several sums in terms of the beta function and its partial derivatives, polygamma functions, the Gauss hypergeometric function, and a determinant. These results generalize known ones in combinatorics. This preprint has been formally published as "Feng Qi and Chuan-Jun Huang, Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales Serie A Matematicas, Vol. 114, Paper No. 191, 9 pages (2020); available online at https://doi.org/10.1007/s13398-020-00927-y."

scholarly journals Riccati Generalized Resonant States of Higher-order Nonlinear Schrӧdinger Equation With Pӧschl-teller Potential

2021 ◽  
Author(s):  
Nisha Kadian ◽  
Sanjana Bhatia ◽  
Shailza Pathania ◽  
Amit Goyal ◽  
Nagaraja Kumar Choragudi
Keyword(s):  
Hypergeometric Functions ◽  
Resonant State ◽  
Higher Order ◽  
Hamiltonian Approach ◽  
Localized Solutions ◽  
Resonant States

Abstract We present resonant state solutions of the higher-order nonlinear Schrӧdinger model, with Pӧschl-Teller (PT) potential, under certain parametric conditions. It is found that the localized solutions can be expressed in terms of the hypergeometric functions F(a, b, c; z). The dynamics of these resonant states and their control using isospectral Hamiltonian approach is well illustrated for PT potential, which is analytically tractable.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Sign in / Sign up

Export Citation Format

Share Document