New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Hamiltonian-Cycle-Decomposition As Hyper Decompress On Super Decompensation
Henry Garrett · Zenodo (CERN European Organization for Nuclear Research) · 2023
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Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a {\tiny Hamiltonian-Cycle-Decomposition} 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-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} if the following expression is called Neutrosophic e-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} criteria holds \begin{eqnarray*} && \forall E'\in C: C~\text{is} \\&& \text{a SuperHyperCycle and it has} \\&& \text{the maximum number of SuperHyperVertices}; \end{eqnarray*} Neutrosophic re-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} if the following expression is called Neutrosophic e-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} criteria holds \begin{eqnarray*} && \forall E'\in C: C~\text{is} \\&& \text{a SuperHyperCycle and it has} \\&& \text{the maximum number of SuperHyperVertices}; \end{eqnarray*} and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} if the following expression is called Neutrosophic v-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} criteria holds \begin{eqnarray*} && \forall V'\in C: C~\text{is} \\&& \text{a SuperHyperCycle and it has} \\&& \text{the maximum number of SuperHyperVertices}; \end{eqnarray*} Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} if the following expression is called Neutrosophic v-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} criteria holds \begin{eqnarray*} && \forall V'\in C: C~\text{is} \\&& \text{a SuperHyperCycle and it has} \\&& \text{the maximum number of SuperHyperVertices}; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} if it's either of Neutrosophic e-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}, Neutrosophic re-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}, Neutrosophic v-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}, and Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}. ((Neutrosophic) SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}). 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 SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} if it's either of Neutrosophic e-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}, Neutrosophic re-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}, Neutrosophic v-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}, and Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} 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 SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}; a Neutrosophic SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} if it's either of Neutrosophic e-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}, Neutrosophic re-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}, Neutrosophic v-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}, and Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} 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 SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}; an Extreme SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} SuperHyperPolynomial if it's either of Neutrosophic e-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}, Neutrosophic re-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}, Neutrosophic v-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}, and Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} 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 SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} SuperHyperPolynomial if it's either of Neutrosophic e-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}, Neutrosophic re-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}, Neutrosophic v-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}, and Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} 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 SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition} if it's either of Neutrosophic e-SuperHyper{\tiny Hamiltonian-Cycle-Decomposition}, Neutrosophic re-SuperHyper{\tiny Hamiltonian-C