Strong Paths Defining Connectivities in Neutrosophic Graphs
| Main Author: | Henry Garrett |
|---|---|
| Format: | Article Journal |
| Bahasa: | eng |
| Terbitan: |
, 2022
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/6480212 |
Daftar Isi:
- New setting is introduced to study strongest number and neutrosophic strongest number arising from length and strength of paths in neutrosophic graphs assigned to couple of vertices and to neutrosophic graphs. Forming neutrosophic paths from a sequence of consecutive vertices forming different types of paths in the terms of length and maximum values of edges forming it to get minmum number to assign to neutrosophic graphs and couple of vertices, is key type of approach to have these notions namely strongest number and neutrosophic strongest number arising from length and strength of paths in neutrosophic graphs assigned to couple of vertices and to neutrosophic graphs. Two numbers and two different paths are assigned to couple of vertices and to neutrosophic graphs, 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 paths in the terms of length and maximum values of edges forming it to get minimum number to assign to neutrosophic graphs and couple of vertices. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then a path from x to y is called strongest path if its length is minimum. This length is called strongest number amid x and y. The maximum number amid all vertices is called strongest number of NTG : (V,E,σ,μ) and it’s denoted by S(NTG); a path from x to y is called neutrosophic strongest path if its strength is μ(uv) which is greater than all strengths of all paths from x to y where x, · · · , u, v, · · · , y is a path. This strength is called neutrosophic strongest number amid x and y. The minimum number amid all vertices is called neutrosophic strongest number of NTG : (V,E,σ,μ) and it’s denoted by Sn(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 strongest Number,” and “Setting of Neutrosophic strongest Number,” for introduced results and used classes. This approach facilitates identifying vertices which form strongest number and neutrosophic strongest number arising from length and strength of paths in neutrosophic graphs assigned to couple of vertices 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 strongest number and neutrosophic strongest number but the sequence has eligibility to define strongest path and neutrosophic strongest path. Some results get more frameworks and perspective about these definitions. The way in that, sequence of consecutive vertices forming different types of paths in the terms of length and maximum values of edges forming it to get minimum number to assign to neutrosophic graphs and couple of vertices, 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 path connectivity is applied in 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.