Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer’s Treatments
Authors: Garrett Henry 
Published: December 2022

In this research, new setting is introduced for new notions, namely, SuperHyperDegree and Co-SuperHyperDegree. Two different types of definitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The cancer&rsquo;s treatments are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called &ldquo;SuperHyperVertex&rdquo; but the relations amid them all officially called &ldquo;SuperHyperEdge&rdquo;. The frameworks &ldquo;SuperHyperGraph&rdquo; and &ldquo;neutrosophic SuperHyperGraph&rdquo; are chosen and elected to research about &ldquo;cancer&rsquo;s treatments&rdquo;. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and &ldquo;cancer&rsquo;s treatments&rdquo;. Some avenues are posed to pursue this research. It&rsquo;s also officially collected in the form of some questions and some problems. If there&rsquo;s a SuperHyperEdge between two SuperHyperVertices, then these two SuperHyperVertices are called SuperHyperNeighbors. The number of SuperHyperNeighbors for a given SuperHyperVertex is called SuperHyperDegree. The number of common SuperHyperNeighbors for some SuperHyperVertices is called Co-SuperHyperDegree for them and used SuperHyperVertices are called Co-SuperHyperNeighbors. A graph is SuperHyperUniform if it&rsquo;s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It&rsquo;s SuperHyperPath if it&rsquo;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it&rsquo;s SuperHyperCycle if it&rsquo;s only one SuperVertex as intersection amid two given SuperHyperEdges; it&rsquo;s SuperHyperStar it&rsquo;s only one SuperVertex as intersection amid all SuperHyperEdges; it&rsquo;s SuperHyperBipartite it&rsquo;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it&rsquo;s SuperHyperMultiPartite it&rsquo;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it&rsquo;s SuperHyperWheel if it&rsquo;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The number of SuperHyperEdges for a given SuperHyperVertex is called SuperHyperDegree. The number of common SuperHyperEdges for some SuperHyperVertices is called Co-SuperHyperDegree for them. The number of SuperHyperVertices for a given SuperHyperEdge is called SuperHyperDegree. The number of common SuperHyperVertices for some SuperHyperEdges is called Co-SuperHyperDegree for them. The model proposes the specific designs. The model is officially called &ldquo;SuperHyperGraph&rdquo; and &ldquo;Neutrosophic SuperHyperGraph&rdquo;. In this model, The &ldquo;specific&rdquo; cells and &ldquo;specific group&rdquo; of cells are modeled as &ldquo;SuperHyperVertices&rdquo; and the common and intended properties between &ldquo;specific&rdquo; cells and &ldquo;specific group&rdquo; of cells are modeled as &ldquo;SuperHyperEdges&rdquo;. Sometimes, it&rsquo;s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise model which in this case the model is called &ldquo;neutrosophic&rdquo;. In the future research, the foundation will be based on the caner&rsquo;s treatment and the results and the definitions will be introduced in redeemed ways. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.