scholarly journals Matroid And Its Outlines

2021 ◽  
Author(s):  
Henry Garrett
Keyword(s):  
Graph Theory ◽  
Set Theory ◽  
Independent Set ◽  
Minimal Set ◽  
Fundamental Parameters ◽  
As If

In this article, there's an effort to make sense about the new versions of matroid. I believe that there's new idea on the background of. matroid. Two styles of matroid is defined in the background of fixed graphs and after that the attributes of these new notion on the graph and its parameters have been studied. The focus of this article is on the version of matroid which has the basis on the cycles as if there's gentle discussion on the results which are based on the set of independent vertices as matroid-x. The relation amid fundamental parameters and specific set like independent set and minimal set in the terminology of graph theory have been considered. Matroid is the word to use in the study on the parameters of graph theory as if set theory and its terminology are also recorded. The terms of word in various terminology have been relatively used. There are open ways to use hypergraphs or some serious relations amid these two types.

scholarly journals SNF: Synthesizing high performance NFV service chains

2016 ◽  
Author(s):  
Georgios P Katsikas ◽  
Marcel Enguehard ◽  
Maciej Kuźniar ◽  
Gerald Q Maguire Jr. ◽  
Dejan Kostić
Keyword(s):  
Set Theory ◽  
High Performance ◽  
State Of The Art ◽  
Cross Layer ◽  
Minimal Set ◽  
Internet Service ◽  
Service Chain ◽  
Network Function ◽  
Network Functions ◽  
Baseline State

In this paper we introduce SNF, a framework that synthesizes (S) network function (NF) service chains by eliminating redundant I/O and repeated elements, while consolidating stateful cross layer packet operations across the chain. SNF uses graph composition and set theory to determine traffic classes handled by a service chain composed of multiple elements. It then synthesizes each traffic class using a minimal set of new elements that apply single-read-single-write and early-discard operations. Our SNF prototype takes a baseline state-of-the-art network functions virtualization (NFV) framework to the level of performance required for practical NFV service deployments. Software-based SNF realizes long (up to 10 NFs) and stateful service chains that achieve line-rate 40 Gbps throughput (up to 8.5x greater than the baseline NFV framework). Hardware-assisted SNF, using a commodity OpenFlow switch, shows that our approach scales at 40 Gbps for Internet Service Provider-level NFV deployments.

Optimizational Model of Transit Line Chosen

2012 ◽  
Vol 178-181 ◽  
pp. 1887-1890
Author(s):  
Wen Bin Liu
Keyword(s):  
Graph Theory ◽  
Computational Model ◽  
Set Theory ◽  
Search Algorithm ◽  
Timing Function ◽  
Left And Right ◽  
Walking Time

In the paper,using graph theory,set theory and iteration,we give gradual search algorithm with number of transfer acting as parameter. Through dealing with data of traffic line, line is united in algorithm,and computational model is simplified. Through optimization of left and right in circuit site and same line repeating site, the shortest timing function in circuit is realized. We consider the subway and walking time of all sites furtherly.

scholarly journals Soft covering based rough graphs and corresponding decision making

2019 ◽  
Vol 17 (1) ◽  
pp. 423-438
Author(s):  
Choonkil Park ◽  
Nasir Shah ◽  
Noor Rehman ◽  
Abbas Ali ◽  
Muhammad Irfan Ali ◽  
...  
Keyword(s):  
Decision Making ◽  
Graph Theory ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Soft Set ◽  
Basic Properties

Abstract Soft set theory and rough set theory are two new tools to discuss uncertainty. Graph theory is a nice way to depict certain information. Particularly soft graphs serve the purpose beautifully. In order to discuss uncertainty in soft graphs, some new types of graphs called soft covering based rough graphs are introduced. Several basic properties of these newly defined graphs are explored. Applications of soft covering based rough graphs in decision making can be very fruitful. In this regard an algorithm has been proposed.

scholarly journals Acyclic subgraph is hard

2018 ◽  
Author(s):  
Thinh D. Nguyen
Keyword(s):  
Graph Theory ◽  
Independent Set ◽  
Acyclic Subgraph

We prove the hardness of yet another problem in graph theory, namely Acyclic Subgraph. A reduction from Independent Set shows that our claim holds.

scholarly journals Disjoint Genus-0 Surfaces in Extremal Graph Theory and Set Theory Lead To a Novel Topological Theorem

2021 ◽  
Author(s):  
Arturo Tozzi
Keyword(s):  
Graph Theory ◽  
Set Theory ◽  
Extremal Graph Theory ◽  
Topological Manifold ◽  
Tree Graph ◽  
Extremal Set Theory ◽  
Extremal Set ◽  
Cycle Graph ◽  
Topological Theorem ◽  
Theory Lead

When an edge is removed, a cycle graph Cn becomes a n-1 tree graph. This observation from extremal set theory leads us to the realm of set theory, in which a topological manifold of genus-1 turns out to be of genus-0. Starting from these premises, we prove a theorem suggesting that a manifold with disjoint points must be of genus-0, while a manifold of genus-1 cannot encompass disjoint points.

scholarly journals Comparison of Two Network-Theory-Based Methods for detecting Functional Regions

2020 ◽  
Vol 11 (2) ◽  
pp. 21-35
Author(s):  
Samo Drobne ◽  
Alberto Garre ◽  
Eloy Hontoria ◽  
Miha Konjar
Keyword(s):  
Graph Theory ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Network Theory ◽  
Urban Region ◽  
Functional Regions ◽  
Important Basis ◽  
Home Region

AbstractBackground: Functional regions are abstract, uniformly defined territorial units that form an important basis for many development strategies of a country or a region.Objectives: This study analyses the application of network theory to the detection of such regions.Methods/Approach: Functional regions are analysed using two methods based on the graph theory: the Walktrap algorithm and the chain approach. The quality of the two regionalization methods is analysed using the fuzzy set theory with the revised method. Slovenia was used as a case study.Results: The Walktrap algorithm generated eight functional regions; seven of them corresponded to those identified in previous studies. The only difference occurred in the northwestern mountainous part of Slovenia. The chain approach led to similar results, although it resulted in a huge functional urban region of the capital Ljubljana.Conclusions: The results show that the Walktrap algorithm calculates regions that are more closed, where more workers find work in the home region, than the chain approach.

scholarly journals Maximal independent sets in bipartite graphs with at least one cycle

2013 ◽  
Vol Vol. 15 no. 2 (Graph Theory) ◽  
Author(s):  
Shuchao Li ◽  
Huihui Zhang ◽  
Xiaoyan Zhang
Keyword(s):  
Graph Theory ◽  
Independent Set ◽  
Independent Sets ◽  
Bipartite Graphs ◽  
Proper Subset ◽  
Maximal Independent Set ◽  
Extremal Graphs ◽  
International Audience ◽  
Maximal Independent Sets ◽  
Disconnected Graphs

Graph Theory International audience A maximal independent set is an independent set that is not a proper subset of any other independent set. Liu [J.Q. Liu, Maximal independent sets of bipartite graphs, J. Graph Theory, 17 (4) (1993) 495-507] determined the largest number of maximal independent sets among all n-vertex bipartite graphs. The corresponding extremal graphs are forests. It is natural and interesting for us to consider this problem on bipartite graphs with cycles. Let \mathscrBₙ (resp. \mathscrBₙ') be the set of all n-vertex bipartite graphs with at least one cycle for even (resp. odd) n. In this paper, the largest number of maximal independent sets of graphs in \mathscrBₙ (resp. \mathscrBₙ') is considered. Among \mathscrBₙ the disconnected graphs with the first-, second-, \ldots, \fracn-22-th largest number of maximal independent sets are characterized, while the connected graphs in \mathscrBₙ having the largest, the second largest number of maximal independent sets are determined. Among \mathscrBₙ' graphs have the largest number of maximal independent sets are identified.

scholarly journals A Formal Framework for Cognitive Models of Multitasking

2020 ◽  
Author(s):  
Michael Lesnick ◽  
Sebastian Musslick ◽  
Biswadip Dey ◽  
Jonathan D. Cohen
Keyword(s):  
Graph Theory ◽  
Success Rate ◽  
Set Theory ◽  
Stroop Task ◽  
Recent Literature ◽  
Cognitive Models ◽  
Formal Framework ◽  
Formal Definitions ◽  
Mathematical Foundations

This note introduces mathematical foundations for modeling of human multitask performance. Using basic definitions from set theory and graph theory, we introduce formal definitions of the environment in which multitasks are performed, of an agent which attempts to perform a multitask, and of the success rate of the agent on a multitask. Drawing on the recent literature on modeling of multitasking, we give two simple examples of multitasking agents, and illustrate the performance of these agents on two multitasking problems: the well-known Stroop task, and a more complex variant.

scholarly journals Certain Properties of Domination in Product Vague Graphs With an Application in Medicine

2021 ◽  
Vol 9 ◽  
Author(s):  
Xiaolong Shi ◽  
Saeed Kosari
Keyword(s):  
Graph Theory ◽  
Real World ◽  
Dominating Set ◽  
Independent Set ◽  
Fuzzy Graph ◽  
Medical Sciences ◽  
Total Dominating Set ◽  
Fuzzy Graphs ◽  
Vague Graph ◽  
Real World Problems

The product vague graph (PVG) is one of the most significant issues in fuzzy graph theory, which has many applications in the medical sciences today. The PVG can manage the uncertainty, connected to the unpredictable and unspecified data of all real-world problems, in which fuzzy graphs (FGs) will not conceivably ensue into generating adequate results. The limitations of previous definitions in FGs have led us to present new definitions in PVGs. Domination is one of the highly remarkable areas in fuzzy graph theory that have many applications in medical and computer sciences. Therefore, in this study, we introduce distinctive concepts and properties related to domination in product vague graphs such as the edge dominating set, total dominating set, perfect dominating set, global dominating set, and edge independent set, with some examples. Finally, we propose an implementation of the concept of a dominating set in medicine that is related to the COVID-19 pandemic.

scholarly journals Max-independent set and the quantum alternating operator ansatz

2020 ◽  
Vol 18 (04) ◽  
pp. 2050011 ◽  
Author(s):  
Zain Hamid Saleem
Keyword(s):  
Graph Theory ◽  
Probability Distribution ◽  
Independent Set ◽  
Independent Sets ◽  
Maximum Independent Set ◽  
Initial State ◽  
Max Cut Problem ◽  
Initial States ◽  
Circuit Depth ◽  
Ring Graph

The maximum-independent set (MIS) problem of graph theory using the quantum alternating operator ansatz is studied. We perform simulations on the Rigetti Forest simulator for the square ring, [Formula: see text], and [Formula: see text] graphs and analyze the dependence of the algorithm on the depth of the circuit and initial states. The probability distribution of observation of the feasible states representing maximum-independent sets is observed to be asymmetric for the MIS problem, which is unlike the Max-Cut problem where the probability distribution of feasible states is symmetric. For asymmetric graphs, it is shown that the algorithm clearly favors the independent set with the larger number of elements even for finite circuit depth. We also compare the approximation ratios for the algorithm when we choose different initial states for the square ring graph and show that it is dependent on the choice of the initial state.

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