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Degree-Based Indices of Some Complex Networks

Lei Ding, Syed Ahtsham Ul Haq Bokhary, Masood Ur Rehman, Usman Ali, Hirra Mubeen, Quaid Iqbal, Jia-Bao Liu, Ahmet Sinan Cevik
2021 Journal of Mathematics  
A topological index is a numeric quantity assigned to a graph that characterizes the structure of a graph.  ...  Topological indices and physico-chemical properties such as atom-bond connectivity ABC , Randić, and geometric-arithmetic index GA are of great importance in the QSAR/QSPR analysis and are used to estimate  ...  For different molecular families, several researchers have shown different computational and theoretical results related to certain topological indices and related them with energies of the graphs.  ... 
doi:10.1155/2021/5531357 fatcat:d7h7uuqfizclvmhrjivhh6za5y

Introducing New Exponential Zagreb Indices for Graphs

Nihat Akgunes, Busra Aydin, Efthymios G. Tsionas
2021 Journal of Mathematics  
After that, in terms of exponential Zagreb indices, lists on equality results over special graphs are presented as well as some new bounds on unicyclic, acyclic, and general graphs are obtained.  ...  New graph invariants, named exponential Zagreb indices, are introduced for more than one type of Zagreb index.  ...  in mathematics and mathematical chemistry. e organization of this paper is as follows.  ... 
doi:10.1155/2021/6675321 fatcat:yxqie34qsbazdn6mr74npkekt4

International Journal of Mathematical Combinatorics, vol. 1/2015

Linfan Mao
2018 Figshare  
geometry and topology and their applications to other sciences.  ...  100-150 pages approx. per volume, which publishes original researchpapers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean  ...  Definition 4. 3 3 The oldest and most investigated topological graph indices are defined as: FirstZagreb index M 1 (G) = v∈V (G) (d G (v)) 2 , second Zagreb index M 2 (G) = uv∈E(G) (d G (u)d G (v))and  ... 
doi:10.6084/m9.figshare.6198917 fatcat:toihd32iunggrjwvtd3wbji424

International Journal Of Mathematical Combinatorics, Vol.4 [article]

Mao, Linfan (Editor-in-Chief)
2010 Zenodo  
geometry and topology and their applications to other sciences.  ...  460 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean  ...  Ivanov and others did much work on semisymmetric graphs (see [2] [3] [8] [9] [10] 13] ). They gave new constructions of such graphs and nearly solved all of Folkman's open problems.  ... 
doi:10.5281/zenodo.8808 fatcat:fsjaqcxutrfajefimgl54db4ri

Reference list of indexed articles

2000 Discrete Applied Mathematics  
Regal, Determining structural similarity of chemicals using graph-theoretic indices 19 (1988) 1744 501. J.D. Benstock, D.J. Bemdt and K.K.  ...  Sen and H.D. Sherali, A branch and bound algorithm for extreme point mathematical programming problems 11 (1985) 265-280 312. G.  ... 
doi:10.1016/s0166-218x(00)00209-2 fatcat:l53yxlj45ffdrdecl3uah2gj3y

International Journal Of Mathematical Combinatorics, Volume 4, 2010 [article]

Mao, Linfan (Editor-in-Chief)
2010 Zenodo  
geometry and topology and their applications to other sciences.  ...  460 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean  ...  Acknowledgement We are thankful to the National Board for Higher Mathematics, Mumbai, for its support through the project 48/5/2008/R&D-II/561, awarded to the first author. We are also thankful to G.  ... 
doi:10.5281/zenodo.9120 fatcat:qlcxqywulnehxhpvizgdfuczty

On the Extremal Wiener Polarity Index of Hückel Graphs

Hongzhuan Wang
2016 Computational and Mathematical Methods in Medicine  
TheWiener polarity indexWp(G)of a graphGis the number of unordered pairs of verticesu,vofGsuch that the distance betweenuandvis equal to 3.  ...  The trees and unicyclic graphs with perfect matching, of which all vertices have degrees not greater than three, are referred to as theHückel treesandunicyclic Hückel graphs, respectively.  ...  Acknowledgments The research was supported by NSF of the Higher Education Institutions of Jiangsu Province (no. 12KJB110001) and NNSF of China (no. 11571135).  ... 
doi:10.1155/2016/3873597 pmid:27247613 pmcid:PMC4876216 fatcat:iklbo54fojcrvoib5pawx7ifma

The Fan–Raspaud conjecture: A randomized algorithmic approach and application to the pair assignment problem in cubic networks

Piotr Formanowicz, Krzysztof Tanaś
2012 International Journal of Applied Mathematics and Computer Science  
Another possible application of the algorithms is that of being a tool for mathematicians working in the field of cubic graph theory, for discovering edge colorings with certain mathematical properties  ...  We show a randomized algorithmic way of finding Fan–Raspaud colorings of a given cubic graph and, analyzing the computer results, we try to find and describe the Fan–Raspaud colorings for some selected  ...  Cubic network as a computer network topology. A cubic network is one of the possible topologies for computer networks. The mathematical model of such a network is a cubic graph.  ... 
doi:10.2478/v10006-012-0057-y fatcat:4hmv2f35ivgwfptplv3zo5um6m

Gap sets for the spectra of cubic graphs

Alicia Kollár, Peter Sarnak
2021 Communications of the American Mathematical Society  
It is known that the gap intervals ( 2 2 , 3 ) (2 \sqrt {2},3) and [ − 3 , − 2 ) [-3,-2) achieved in cubic Ramanujan graphs and line graphs are maximal.  ...  We also show that every point in [ − 3 , 3 ) [-3,3) can be gapped by planar cubic graphs. Our results show that the study of spectra of cubic, and even planar cubic, graphs is subtle and very rich.  ...  Flammia, and F. Wei for instructive discussions related to this work.  ... 
doi:10.1090/cams/3 fatcat:7cerdedcrbg5rl6l3iko5bdso4

Learning on Random Balls is Sufficient for Estimating (Some) Graph Parameters [article]

Takanori Maehara, Hoang NT
2021 arXiv   pre-print
Equipped with insights from graph limit theory, we propose a new graph classification model that works on a randomly sampled subgraph and a novel topology to characterize the representability of the model  ...  In this work, we develop a theoretical framework for graph classification problems in the partial observation setting (i.e., subgraph samplings).  ...  Acknowledgement We would like to thank the anonymous reviewers and the area chairs for their thoughtful comments which help us improve our manuscript.  ... 
arXiv:2111.03317v1 fatcat:aqw4ljok6rhpdfikuxekqn2q5e

On the Origin of Biomolecular Networks

Heeralal Janwa, Steven E. Massey, Julian Velev, Bud Mishra
2019 Frontiers in Genetics  
graph theoretic lens.  ...  Information asymmetry between sender and receiver genes is identified as a key feature distinguishing early biochemical reactions from abiotic chemistry, and a driver of network topology as biomolecular  ...  The girth g(G), is the shortest cycle in G. A walk whose vertices are distinct is called a (simple) path. The concept of a walk allows us to define other properties of the graph.  ... 
doi:10.3389/fgene.2019.00240 pmid:31024611 pmcid:PMC6467946 fatcat:auvvb24ugvcm3g7xs362xlyneu

Automated conjecturing I: Fajtlowicz's Dalmatian heuristic revisited

C.E. Larson, N. Van Cleemput
2016 Artificial Intelligence  
Conjectures in matrix theory, number theory, and graph theory are reported, together with an experiment in using conjectures to automate game play.  ...  We discuss a new implementation of, and new experiments with, Fajtlowicz's Dalmatian conjecture-making heuristic.  ...  For acyclic graphs, girth was set to infinity. The Szeged and Wiener indices are of special interest in chemical graph theory.  ... 
doi:10.1016/j.artint.2015.10.002 fatcat:gu6kvb5ajzh6nldfcmu2qgnqbe

Same Stats, Different Graphs: Exploring the Space of Graphs in Terms of Graph Properties

Hang Chen, Stephen G. Kobourov, Ross Maciejewski, Yafeng Lu, Vahan Huroyan, Utkarsh Soni
2019 IEEE Transactions on Visualization and Computer Graphics  
We consider a similar problem in the context of graph mining.  ...  We also describe a method for generating many graphs that are identical over a number of graph properties and statistics yet are clearly different and identifiably distinct.  ...  Other interesting open problems that arise from this work include: designing efficient generators for graphs with the same stats or graphs that share some stats and vary in others, finding theoretical  ... 
doi:10.1109/tvcg.2019.2946558 pmid:31603821 fatcat:nqhlch3apfb4jcntn7zr7dpypm

Sharp bounds for the modified multiplicative Zagreb indices of graphs with vertex connectivity at most k

Haiying Wang, Shaohui Wang, Bing Wei
2019 Filomat  
Zagreb indices and their modified versions of a molecular graph originate from many practical problems such as two dimensional quantitative structure-activity (2D QSAR) and molecular chirality.  ...  Our results enrich outcomes on studying Zagreb indices and the methods developed in this paper may provide some new tools for investigating the values on modified multiplicative Zagreb indices of other  ...  Acknowledgments The authors would like to thank Editor Paola Bonacini and the referees for providing their valuable comments and suggestions, which lead to great improvements in writing of this paper.  ... 
doi:10.2298/fil1914673w fatcat:ri42u44dynf45opheml7lbxdum

Graph Theoretic Models in Chemistry and Molecular Biology [chapter]

Debra Knisley, Jeff Knisley
Handbook of Applied Algorithms  
Figure 3 .1 shows two drawings of the same graph that can be described both as a cycle on six vertices and as a bipartite graph. The two graphs in Figure 3 .1 are said to be isomorphic.  ...  In general, it is a difficult problem to determine if two graphs are isomorphic. An alternate definition of a graph is a set of elements with a well-defined relation.  ...  Since we are primarily concerned with graph theoretic models, we will focus on 2D descriptors from graphs and refer to these as topological descriptors or topological indices.  ... 
doi:10.1002/9780470175668.ch3 fatcat:kfzdr7n7s5e47nxrvmeltun3ji
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