Connectivities of Neutrosophic Graphs in the terms of Crisp Cycles
| Main Author: | Henry Garrett |
|---|---|
| Format: | Article Journal |
| Bahasa: | eng |
| Terbitan: |
, 2022
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/6490403 |
Daftar Isi:
- New setting is introduced to study connectivity number and neutrosophic connectivity number arising from length and strength of cycles in neutrosophic graphs assigned to one vertex and to neutrosophic graphs. Consider a vertex. Maximum strengths of all cycles based on that vertex is a number which is representative strength based on that vertex. Minimum number amid all representative numbers is called neutrosophic connectivity number. Forming cycles from a sequence of consecutive vertices to figure out different types of cycles in the terms of length and maximum values of edges to get minimum number to assign to neutrosophic graphs and a vertex, is key type of approach to have these notions namely connectivity number and neutrosophic connectivity number arising from length and strength of cycles in neutrosophic graphs assigned to one vertex and to neutrosophic graphs. Two numbers and two different cycles are assigned to a vertex and to a neutrosophic graph, are obtained but now both settings lead to approach is on demand which is to compute and to find sequence of consecutive vertices forming different types of cycles in the terms of length and maximum values of edges forming it to get minimum number to assign to a neutrosophic graph and to a vertex. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then a cycle based on x is called cyclic connectivity if its length is minimum. This length is called connectivity number based on x. The maximum number amid all vertices is called connectivity number of NTG : (V,E,σ,μ) and it’s denoted by C(NTG); a cycle based on x is called neutrosophic cyclic connectivity if its strength is is greater than all strengths of all cycles based on x. This strength is called neutrosophic connectivity number based on x. The minimum number amid all vertices is called neutrosophic connectivity number of NTG : (V,E,σ,μ) and it’s denoted by Cn(NTG). As concluding results, there are some statements, remarks, examples and clarifications about some classes of strong-neutrosophic graphs namely strong-path-neutrosophic graphs, strong-cycle-neutrosophic graphs, strong-complete-neutrosophic graphs, strong-star-neutrosophic graphs, strong-complete-bipartite-neutrosophic graphs, strong-complete-t-partite-neutrosophic graphs and strong-wheel-neutrosophic graphs. The clarifications are also presented in both sections “Setting of connectivity number,” and “Setting of neutrosophic connectivity number,” for introduced results and used classes. This approach facilitates identifying vertices which form connectivity number and neutrosophic connectivity number arising from length and strength of cycles in neutrosophic graphs assigned to one vertex and to neutrosophic graphs. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. The value of an edge has eligibility to define connectivity number and neutrosophic connectivity number but the sequence has eligibility to define cyclic connectivity and neutrosophic cyclic connectivity. Some results get more frameworks and perspective about these definitions. The way in that, sequence of consecutive vertices forming different types of cycles in the terms of length and maximum values of edges forming it to get minimum number to assign to neutrosophic graphs and a vertex or in other words, the way in that, consider a vertex. Maximum strengths of all cycles based on that vertex is a number which is representative strength based on that vertex. Minimum number amid all representative numbers is called neutrosophic connectivity number, opens the way to do some approaches. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Neutrosophic cycle connectivity is applied to different settings and classes of neutrosophic graphs. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.