scholarly journals On BC-Subtrees in Multi-Fan and Multi-Wheel Graphs

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 36
Author(s):  
Yu Yang ◽  
Long Li ◽  
Wenhu Wang ◽  
Hua Wang
Keyword(s):  
Structural Properties ◽  
Generating Functions ◽  
Topological Index ◽  
Extremal Problems ◽  
Distance Constraint ◽  
Wheel Graphs ◽  
Recursive Formulas ◽  
Cyclic Graphs ◽  
New Perspective

The BC-subtree (a subtree in which any two leaves are at even distance apart) number index is the total number of non-empty BC-subtrees of a graph, and is defined as a counting-based topological index that incorporates the leaf distance constraint. In this paper, we provide recursive formulas for computing the BC-subtree generating functions of multi-fan and multi-wheel graphs. As an application, we obtain the BC-subtree numbers of multi-fan graphs, r multi-fan graphs, multi-wheel (wheel) graphs, and discuss the change of the BC-subtree numbers between different multi-fan or multi-wheel graphs. We also consider the behavior of the BC-subtree number in these structures through the study of extremal problems and BC-subtree density. Our study offers a new perspective on understanding new structural properties of cyclic graphs.

scholarly journals On Subtree Number Index of Generalized Book Graphs, Fan Graphs, and Wheel Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Daoqiang Sun ◽  
Zhengying Zhao ◽  
Xiaoxiao Li ◽  
Jiayi Cao ◽  
Yu Yang
Keyword(s):  
Structural Analysis ◽  
Structural Properties ◽  
Generating Function ◽  
Generating Functions ◽  
Asymptotic Properties ◽  
Wheel Graphs

With generating function and structural analysis, this paper presents the subtree generating functions and the subtree number index of generalized book graphs, generalized fan graphs, and generalized wheel graphs, respectively. As an application, this paper also briefly studies the subtree number index and the asymptotic properties of the subtree densities in regular book graphs, regular fan graphs, and regular wheel graphs. The results provide the basis for studying novel structural properties of the graphs generated by generalized book graphs, fan graphs, and wheel graphs from the perspective of the subtree number index.

scholarly journals Catalan words avoiding pairs of length three patterns

2021 ◽  
Vol vol. 22 no. 2, Permutation... (Special issues) ◽  
Author(s):  
Jean-Luc Baril ◽  
Carine Khalil ◽  
Vincent Vajnovszki
Keyword(s):  
Structural Properties ◽  
Generating Functions ◽  
Recursive Decomposition ◽  
Integer Sequence ◽  
Combinatorial Interpretations

Catalan words are particular growth-restricted words counted by the eponymous integer sequence. In this article we consider Catalan words avoiding a pair of patterns of length 3, pursuing the recent initiating work of the first and last authors and of S. Kirgizov where (among other things) the enumeration of Catalan words avoiding a patterns of length 3 is completed. More precisely, we explore systematically the structural properties of the sets of words under consideration and give enumerating results by means of recursive decomposition, constructive bijections or bivariate generating functions with respect to the length and descent number. Some of the obtained enumerating sequences are known, and thus the corresponding results establish new combinatorial interpretations for them.

A general construction of mutually orthogonal latin squares of prime order

2018 ◽  
Vol 7 (1-2) ◽  
pp. 77-93
Author(s):  
J. A. Saka ◽  
O. O. Oyadare
Keyword(s):  
Structural Properties ◽  
Generating Function ◽  
Generating Functions ◽  
Prime Order ◽  
Latin Squares ◽  
General Construction ◽  
Orthogonal Latin Squares ◽  
Mutually Orthogonal Latin Squares ◽  
Complete Set ◽  
General Method

This paper presents a general method of constructing a complete set of Mutually Orthogonal Latin Squares (MOLS) of the order of any prime, via the use of generating functions dened on the nite eld of this order. Apart from using the generating function to get a complete set of Mutually Orthogonal Latin Squares, the studies of the generating functions opens up the possibility of getting at the deep structural properties of MOLS. Copious examples were given for detailed illustrations.

scholarly journals On Subtrees of Fan Graphs, Wheel Graphs, and “Partitions” of Wheel Graphs under Dynamic Evolution

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 472 ◽  
Author(s):  
Yu Yang ◽  
An Wang ◽  
Hua Wang ◽  
Wei-Ting Zhao ◽  
Dao-Qiang Sun
Keyword(s):  
Evolutionary Dynamics ◽  
Phylogenetic Reconstruction ◽  
Extremal Problems ◽  
Dynamic Evolution ◽  
Graph Invariants ◽  
Wheel Graphs

The number of subtrees, or simply the subtree number, is one of the most studied counting-based graph invariants that has applications in many interdisciplinary fields such as phylogenetic reconstruction. Motivated from the study of graph surgeries on evolutionary dynamics, we consider the subtree problems of fan graphs, wheel graphs, and the class of graphs obtained from “partitioning” wheel graphs under dynamic evolution. The enumeration of these subtree numbers is done through the so-called subtree generation functions of graphs. With the enumerative result, we briefly explore the extremal problems in the corresponding class of graphs. Some interesting observations on the behavior of the subtree number are also presented.

scholarly journals On Degree-Based Topological Indices for Strong Double Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Muhammad Rafiullah ◽  
Hafiz Muhammad Afzal Siddiqui ◽  
Muhammad Kamran Siddiqui ◽  
Mlamuli Dhlamini
Keyword(s):  
Structural Properties ◽  
Topological Index ◽  
Graphical Representation ◽  
Topological Indices ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Characteristic Value ◽  
3D Graphical Representation

A topological index is a characteristic value which represents some structural properties of a chemical graph. We study strong double graphs and their generalization to compute Zagreb indices and Zagreb coindices. We provide their explicit computing formulas along with an algorithm to generate and verify the results. We also find the relation between these indices. A 3D graphical representation and graphs are also presented to understand the dynamics of the aforementioned topological indices.

scholarly journals Computing FGZ Index of Sum Graphs under Strong Product

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Zhi-Ba Peng ◽  
Saira Javed ◽  
Muhammad Javaid ◽  
Jia-Bao Liu
Keyword(s):  
Structural Properties ◽  
Topological Index ◽  
Molecular Graph ◽  
Chemical Compounds ◽  
Zagreb Index ◽  
Strong Product ◽  
Product Of Graphs

Topological index (TI) is a function that assigns a numeric value to a (molecular) graph that predicts its various physical and structural properties. In this paper, we study the sum graphs (S-sum, R-sum, Q-sum and T-sum) using the subdivision related operations and strong product of graphs which create hexagonal chains isomorphic to many chemical compounds. Mainly, the exact values of first general Zagreb index (FGZI) for four sum graphs are obtained. At the end, FGZI of the two particular families of sum graphs are also computed as applications of the main results. Moreover, the dominating role of the FGZI among these sum graphs is also shown using the numerical values and their graphical presentations.

scholarly journals On Some Properties of Multiplicative Topological Indices in Silicon-Carbon

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Abid Mahboob ◽  
Sajid Mahboob ◽  
Mohammed M. M. Jaradat ◽  
Nigait Nigar ◽  
Imran Siddique
Keyword(s):  
Graph Theory ◽  
Structural Properties ◽  
Topological Index ◽  
Molecular Graph ◽  
Chemical Compounds ◽  
Google Maps ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Silicon Carbon ◽  
Connectivity Indices

The use of graph theory can be visualized in nanochemistry, computer networks, Google maps, and molecular graph which are common areas to elaborate application of this subject. In nanochemistry, a numeric number (topological index) is used to estimate the biological, physical, and structural properties of chemical compounds that are associated with the chemical graph. In this paper, we compute the first and second multiplicative Zagreb indices ( M 1 G and ( M 1 G )), generalized multiplicative geometric arithmetic index ( GA α II G ), and multiplicative sum connectivity and multiplicative product connectivity indices ( SCII G and PCII G ) of SiC 4 − I m , n and SiC 4 − II m , n .

scholarly journals Automatic Classification of Restricted Lattice Walks

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Alin Bostan ◽  
Manuel Kauers
Keyword(s):  
Structural Properties ◽  
Generating Functions ◽  
Automatic Classification ◽  
Experimental Mathematics ◽  
Lattice Walks ◽  
International Audience

International audience We propose an $\textit{experimental mathematics approach}$ leading to the computer-driven $\textit{discovery}$ of various conjectures about structural properties of generating functions coming from enumeration of restricted lattice walks in 2D and in 3D.

scholarly journals Differential Equation and Recursive Formulas of Sheffer Polynomial Sequences

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Heekyung Youn ◽  
Yongzhi Yang
Keyword(s):  
Differential Equation ◽  
Generating Functions ◽  
Matrix Algebra ◽  
Polynomial Sequences ◽  
Recursive Formulas ◽  
The Relationship ◽  
Sheffer Polynomial

We derive a differential equation and recursive formulas of Sheffer polynomial sequences utilizing matrix algebra. These formulas provide the defining characteristics of, and the means to compute, the Sheffer polynomial sequences. The tools we use are well-known Pascal functional and Wronskian matrices. The properties and the relationship between the two matrices simplify the complexity of the generating functions of Sheffer polynomial sequences. This work extends He and Ricci's work (2002) to a broader class of polynomial sequences, from Appell to Sheffer, using a different method. The work is self-contained.

Sign in / Sign up

Export Citation Format

Share Document