K-Number In SuperHyperGraphs
Henry Garrett · Zenodo (CERN European Organization for Nuclear Research) · 2023
“#167 Article” Henry Garrett, “New Ideas On Super Gradient By Hyper k-Class Of SuperHyperK-Number In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.23037.44003). @ResearchGate: https://www.researchgate.net/publication/368753609 @Scribd: https://www.scribd.com/document/627635276 @ZENODO_ORG: https://zenodo.org/record/7672351 @academia: https://www.academia.edu/97431782 — “#168 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers”, ResearchGate 2023, (doi: 10.13140/RG.2.2.33103.76968). @ResearchGate: https://www.researchgate.net/publication/368752952 @Scribd: https://www.scribd.com/document/627632376 @ZENODO_ORG: https://zenodo.org/record/7672331 @academia: https://www.academia.edu/97431255 — — — “#119th Book” || K-Number In SuperHyperGraphs @googlebooks:https://books.google.com/books/about?id=- @GooglePlay:https://play.google.com/store/books/details?id=- @ResearchGate: https://www.researchgate.net/publication/368754006 @WordPress: https://drhenrygarrett.wordpress.com/2023/02/25/K-Number-In-SuperHyperGraphs/ @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia:https://www.academia.edu/- — — “#119th Book” || K-Number In SuperHyperGraphs #Link (Paperback): https://www.amazon.com/dp/B0BW2KJKJD (Hardcover): https://www.amazon.com/dp/B0BW2BSXTG (Kindle Edition): https://www.amazon.com/dp/B0BWMKNH7H #ISBN (Paperback): 9798378647705 (Hardcover): 9798378648146 (Kindle Edition): CC BY-NC-ND 4.0 — In this scientific research book, there are some scientific research chapters on “Extreme K-Number In SuperHyperGraphs ” and “Neutrosophic K-Number In SuperHyperGraphs ” about some scientific researches on K-Number In SuperHyperGraphs by two (Extreme/Neutrosophic) notions, namely, Extreme K-Number In SuperHyperGraphs and Neutrosophic K-Number In SuperHyperGraphs . With scientific researches on the basic properties, the scientific research book starts to make Extreme K-Number In SuperHyperGraphs theory and Neutrosophic K-Number In SuperHyperGraphs theory more (Extremely/Neutrosophicly) understandable. Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in the following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It’s titled “Beyond Neutrosophic Graphs” and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. [Ref] Henry Garrett, (2022). “Beyond Neutrosophic Graphs”, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 978-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in the following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It’s titled “Neutrosophic Duality” and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and K-Number In SuperHyperGraphs in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It’s smart to consider a set but acting on its complement that what’s done in this research book which is popular in the terms of high readers in Scribd. [Ref] Henry Garrett, (2022). “Neutrosophic Duality”, Florida: GLOBAL KNOW- LEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). — “#167 Article” Henry Garrett, “New Ideas On Super Gradient By Hyper k-Class Of SuperHyperK-Number In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.23037.44003). @ResearchGate: https://www.researchgate.net/publication/368753609 @Scribd: https://www.scribd.com/document/627635276 @ZENODO_ORG: https://zenodo.org/record/7672351 @academia: https://www.academia.edu/97431782 — “#168 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers”, ResearchGate 2023, (doi: 10.13140/RG.2.2.33103.76968). @ResearchGate: https://www.researchgate.net/publication/368752952 @Scribd: https://www.scribd.com/document/627632376 @ZENODO_ORG: https://zenodo.org/record/7672331 @academia: https://www.academia.edu/97431255 — — — “#119th Book” || K-Number In SuperHyperGraphs @googlebooks:https://books.google.com/books/about?id=- @GooglePlay:https://play.google.com/store/books/details?id=- @ResearchGate: https://www.researchgate.net/publication/368754006 @WordPress: https://drhenrygarrett.wordpress.com/2023/02/25/K-Number-In-SuperHyperGraphs/ @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia:https://www.academia.edu/- — — “#119th Book” || K-Number In SuperHyperGraphs #Link (Paperback): https://www.amazon.com/dp/B0BW2KJKJD (Hardcover): https://www.amazon.com/dp/B0BW2BSXTG (Kindle Edition): https://www.amazon.com/dp/B0BWMKNH7H #ISBN (Paperback): 9798378647705 (Hardcover): 9798378648146 (Kindle Edition): CC BY-NC-ND 4.0 — — Project: Neutrosophic SuperHyperGraphs and SuperHyperGraphs -- Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay -- \section{Background} There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them date back on February 19, 2023. \\ First article is titled ``properties of SuperHyperGraph and neutrosophic SuperHyperGraph'' in \textbf{Ref.} \cite{HG1} by Henry Garrett (2022). It's first step toward the research on neutrosophic SuperHyperGraphs. This research article is published on the journal ``Neutrosophic Sets and Systems'' in issue 49 and the pages 531-561. In this research article, different types of notions like dominating, resolving, coloring, Eulerian(Hamiltonian) neutrosophic path, n-Eulerian(Hamiltonian) neutrosophic path, zero forcing number, zero forcing neutrosophic- number, independent number, independent neutrosophic-number, clique number, clique neutrosophic-number, matching number, matching neutrosophic-number, girth, neutrosophic girth, 1-zero-forcing number, 1-zero- forcing neutrosophic-number, failed 1-zero-forcing number, failed 1-zero-forcing neutrosophic-number, global- offensive alliance, t-offensive alliance, t-defensive alliance, t-powerful alliance, and global-powerful alliance are defined in SuperHyperGraph and neutrosophic SuperHyperGraph. Some Classes of SuperHyperGraph and Neutrosophic SuperHyperGraph are cases of research. Some results are applied in family of SuperHyperGraph and neutrosophic SuperHyperGraph. Thus this research article has concentrated on the vast notions and introducing the majority of notions. \\ The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs'' in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It's published in prestigious and fancy journal is entitled “Journal of Current Trends in Computer Science Research (JCTCSR)” with ISO abbreviation ``J Curr Trends Comp Sci Res'' in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It's the breakthrough toward independent results based on initial background. \\ The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes'' in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It's published in prestigious and fancy journal is entitled “Journal of Mathematical Techniques and Computational Mathematics(JMTCM)” with ISO abbreviation ``J Math Techniques Comput Math'' in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It's the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer’s Treatments'' in \textbf{Ref.} \cite{HG133} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer’s Treatments. It's published in prestigious and fancy journal is entitled “Journal