New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Vertex-Neighbor As Hyper Nebbish On Super Nebulous
Henry Garrett · Zenodo (CERN European Organization for Nuclear Research) · 2023
“#205 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Vertex-Neighbor As Hyper Nebbish On Super Nebulous”, ResearchGate 2023, (doi: 10.13140/RG.2.2.31366.24641). @ResearchGate: https://www.researchgate.net/publication/369365026 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- Available at @WordPress @ResearchGate @Scribd @academia @ZENODO_ORG @Twitter @facebook @LinkedIn @Amazon @googlebooks @GooglePlay @AmazonKindle \\documentclass[10pt,letterpaper]{article} \\usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \\usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \\usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \\usepackage[utf8]{inputenc} % clean citations \\usepackage{cite} % hyperref makes references clicky. use \\url{www.example.com} or \\href{www.example.com}{description} to add a clicky url \\usepackage{nameref,hyperref} % line numbers \\usepackage[right]{lineno} % improves typesetting in LaTeX \\usepackage{microtype} \\DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \\raggedright \\setlength{\\parindent}{0.5cm} \\textwidth 5.25in \\textheight 8.79in % Remove % for double line spacing %\\usepackage{setspace} %\\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \\usepackage{changepage} % adjust caption style \\usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \\makeatletter \\renewcommand{\\@biblabel}[1]{\\quad#1.} \\makeatother % headrule, footrule and page numbers \\usepackage{lastpage,fancyhdr,graphicx} \\usepackage{epstopdf} \\pagestyle{myheadings} \\pagestyle{fancy} \\fancyhf{} \\rfoot{\\thepage/\\pageref{LastPage}} \\renewcommand{\\footrule}{\\hrule height 2pt \\vspace{2mm}} \\fancyheadoffset[L]{2.25in} \\fancyfootoffset[L]{2.25in} % use \\textcolor{color}{text} for colored text (e.g. highlight to-do areas) \\usepackage{color} % define custom colors (this one is for figure captions) \\definecolor{Gray}{gray}{.25} % this is required to include graphics \\usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \\usepackage{sidecap} \\usepackage{leftidx} % use for have text wrap around figures \\usepackage{wrapfig} \\usepackage[pscoord]{eso-pic} \\usepackage[fulladjust]{marginnote} \\reversemarginpar \ ewtheorem{theorem}{Theorem}[section] \ ewtheorem{lemma}[theorem]{Lemma} \ ewtheorem{proposition}[theorem]{Proposition} \ ewtheorem{corollary}[theorem]{Corollary} \\theoremstyle{definition} \ ewtheorem{definition}[theorem]{Definition} \ ewtheorem{example}[theorem]{Example} \ ewtheorem{xca}[theorem]{Exercise} \\theoremstyle{remark} \ ewtheorem{remark}[theorem]{Remark} \\theoremstyle{observation} \ ewtheorem{observation}[theorem]{Observation} \\theoremstyle{question} \ ewtheorem{question}[theorem]{Question} \\theoremstyle{problem} \ ewtheorem{problem}[theorem]{Problem} \ umberwithin{equation}{section} \\usepackage{fancyhdr} \\pagestyle{fancy} \\fancyhf{} \\fancyhead[LE,RO]{Henry Garrett · Independent Researcher · Department of Mathematics · [email protected] · Manhattan, NY, USA } \\fancyfoot[LE,RO]{Henry Garrett · Independent Researcher · Department of Mathematics · [email protected] · Manhattan, NY, USA } % document begins here \\begin{document} \\vspace*{0.35in} \\linenumbers % title goes here: \\begin{flushleft} {\\Large \\textbf\ ewline{ New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Vertex-Neighbor As Hyper Nebbish On Super Nebulous } } \ ewline \ ewline Henry Garrett · Independent Researcher · Department of Mathematics · [email protected] · Manhattan, NY, USA % authors go here: \\end{flushleft} \\section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperVertex-Neighbor). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a Vertex-Neighbor pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V'=\\{V_1,V_2,\\ldots,V_s\\}$ and $E'=\\{E_1,E_2,\\ldots,E_z\\}.$ Then either $V'$ or $E'$ is called Neutrosophic e-SuperHyperVertex-Neighbor if the following expression is called Neutrosophic e-SuperHyperVertex-Neighbor criteria holds \\begin{eqnarray*} && \\forall E_a\\in E':~N(E_a) \\text{is disconnect-able}; \\end{eqnarray*} Neutrosophic re-SuperHyperVertex-Neighbor if the following expression is called Neutrosophic e-SuperHyperVertex-Neighbor criteria holds \\begin{eqnarray*} && \\forall E_a\\in E':~N(E_a) \\text{is disconnect-able}; \\end{eqnarray*} and $|E_i|_{\\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperVertex-Neighbor if the following expression is called Neutrosophic v-SuperHyperVertex-Neighbor criteria holds \\begin{eqnarray*} && \\forall V_a\\in V':~N(V_a) \\text{is disconnect-able}; \\end{eqnarray*} Neutrosophic rv-SuperHyperVertex-Neighbor if the following expression is called Neutrosophic v-SuperHyperVertex-Neighbor criteria holds \\begin{eqnarray*} && \\forall V_a\\in V':~N(V_a) \\text{is disconnect-able}; \\end{eqnarray*} and $|V_i|_{\\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyperVertex-Neighbor if it's either of Neutrosophic e-SuperHyperVertex-Neighbor, Neutrosophic re-SuperHyperVertex-Neighbor, Neutrosophic v-SuperHyperVertex-Neighbor, and Neutrosophic rv-SuperHyperVertex-Neighbor. ((Neutrosophic) SuperHyperVertex-Neighbor). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\\{V_1,V_2,\\ldots,V_s\\}.$ Then $E$ is called an Extreme SuperHyperVertex-Neighbor if it's either of Neutrosophic e-SuperHyperVertex-Neighbor, Neutrosophic re-SuperHyperVertex-Neighbor, Neutrosophic v-SuperHyperVertex-Neighbor, and Neutrosophic rv-SuperHyperVertex-Neighbor and $\\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the conseNeighborive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperVertex-Neighbor; a Neutrosophic SuperHyperVertex-Neighbor if it's either of Neutrosophic e-SuperHyperVertex-Neighbor, Neutrosophic re-SuperHyperVertex-Neighbor, Neutrosophic v-SuperHyperVertex-Neighbor, and Neutrosophic rv-SuperHyperVertex-Neighbor and $\\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality conseNeighborive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperVertex-Neighbor; an Extreme SuperHyperVertex-Neighbor SuperHyperPolynomial if it's either of Neutrosophic e-SuperHyperVertex-Neighbor, Neutrosophic re-SuperHyperVertex-Neighbor, Neutrosophic v-SuperHyperVertex-Neighbor, and Neutrosophic rv-SuperHyperVertex-Neighbor and $\\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality conseNeighborive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperVertex-Neighbor; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperVertex-Neighbor SuperHyperPolynomial if it's either of Neutrosophic e-SuperHyperVertex-Neighbor, Neutrosophic re-SuperHyperVertex-Neighbor, Neutrosophic v-SuperHyperVertex-Neighbor, and Neutrosophic rv-SuperHyperVertex-Neighbor and $\\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality conseNeighborive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperVertex-Neighbor; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyperVertex-Neighbor if it's either of Neutrosophic e-SuperHyperVertex-Neighbor, Neutrosophic re-SuperHyperVertex-Neighbor, Neutrosophic v-SuperHyperVertex-Neighbor, and Neutrosophic rv-SuperHyperVertex-Neighbor and $\\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the conseNeighborive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperVertex-Neighbor; a Neutrosophic V-SuperHyperVertex-Neighbor if it's either of Neutrosophic e-SuperHyperVertex-Neighbor, Neutrosophic re-SuperHyperVertex-Neighbor, Neutrosophic v-SuperHyperVertex-Neighbor, and Neutrosophic rv-SuperHyperVertex-Neighbor and $\\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality conseNeighborive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutros