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Degree-Based Indices of Some Complex Networks

2021
*
Journal of Mathematics
*

A

doi:10.1155/2021/5531357
fatcat:d7h7uuqfizclvmhrjivhh6za5y
*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*. ...##
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Introducing New Exponential Zagreb Indices for Graphs

2021
*
Journal of Mathematics
*

After that, in terms of exponential Zagreb

doi:10.1155/2021/6675321
fatcat:yxqie34qsbazdn6mr74npkekt4
*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. ...##
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International Journal of Mathematical Combinatorics, vol. 1/2015

2018
*
Figshare
*

geometry

doi:10.6084/m9.figshare.6198917
fatcat:toihd32iunggrjwvtd3wbji424
*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*...##
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International Journal Of Mathematical Combinatorics, Vol.4
[article]

2010
*
Zenodo
*

geometry

doi:10.5281/zenodo.8808
fatcat:fsjaqcxutrfajefimgl54db4ri
*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*. ...##
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Reference list of indexed articles

2000
*
Discrete Applied Mathematics
*

Regal, Determining structural similarity of chemicals using

doi:10.1016/s0166-218x(00)00209-2
fatcat:l53yxlj45ffdrdecl3uah2gj3y
*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*. ...##
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International Journal Of Mathematical Combinatorics, Volume 4, 2010
[article]

2010
*
Zenodo
*

geometry

doi:10.5281/zenodo.9120
fatcat:qlcxqywulnehxhpvizgdfuczty
*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*. ...##
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On the Extremal Wiener Polarity Index of Hückel Graphs

2016
*
Computational and Mathematical Methods in Medicine
*

TheWiener polarity indexWp(

doi:10.1155/2016/3873597
pmid:27247613
pmcid:PMC4876216
fatcat:iklbo54fojcrvoib5pawx7ifma
*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). ...##
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The Fan–Raspaud conjecture: A randomized algorithmic approach and application to the pair assignment problem in cubic networks

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

doi:10.2478/v10006-012-0057-y
fatcat:4hmv2f35ivgwfptplv3zo5um6m
*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*. ...##
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Gap sets for the spectra of cubic graphs

2021
*
Communications of the American Mathematical Society
*

It is known that the gap intervals ( 2 2 ,

doi:10.1090/cams/3
fatcat:7cerdedcrbg5rl6l3iko5bdso4
*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. ...##
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Learning on Random Balls is Sufficient for Estimating (Some) Graph Parameters
[article]

2021
*
arXiv
*
pre-print

Equipped

arXiv:2111.03317v1
fatcat:aqw4ljok6rhpdfikuxekqn2q5e
*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. ...##
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On the Origin of Biomolecular Networks

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*. ...

##
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Automated conjecturing I: Fajtlowicz's Dalmatian heuristic revisited

2016
*
Artificial Intelligence
*

Conjectures in matrix theory, number theory,

doi:10.1016/j.artint.2015.10.002
fatcat:gu6kvb5ajzh6nldfcmu2qgnqbe
*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. ...##
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Same Stats, Different Graphs: Exploring the Space of Graphs in Terms of Graph Properties

2019
*
IEEE Transactions on Visualization and Computer Graphics
*

We consider a similar

doi:10.1109/tvcg.2019.2946558
pmid:31603821
fatcat:nqhlch3apfb4jcntn7zr7dpypm
*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*...##
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Sharp bounds for the modified multiplicative Zagreb indices of graphs with vertex connectivity at most k

2019
*
Filomat
*

Zagreb

doi:10.2298/fil1914673w
fatcat:ri42u44dynf45opheml7lbxdum
*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. ...##
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Graph Theoretic Models in Chemistry and Molecular Biology
[chapter]

*
Handbook of Applied Algorithms
*

Figure

doi:10.1002/9780470175668.ch3
fatcat:kfzdr7n7s5e47nxrvmeltun3ji
*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*. ...
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