Neutrosophic graphs are employed as a mathematical key to hold an imprecise and unspecified data. Vague sets gives more intuitive graphical notation of vague information, that delicates crucially better analysis in data relationships, incompleteness and similarity measures. In this paper, the neutrosophic vague line graphs are introduced. The necessary and sufficient condition for a line graph to be neutrosophic vague line graph is provided. Further, homomorphism, weak vertex and weak line isomorphism are discussed. The given results are illustrated with suitable example.

Neutrosophic vague graphs are employed as a mathematical key to hold an imprecise and unspecified data. Vague sets gives more intuitive graphical notation of vague information, that delicates crucially better analysis in data relationships, incompleteness and similarity measures. In this paper, the neutrosophic bipolar vague line graphs are introduced. The necessary and sufficient condition for a line graph to be neutrosophic bipolar vague line graph is provided. Further, homomorphism, weak vertex and weak line isomorphism are discussed. The given results are illustrated with suitable example.

Neutrosophic Sets and Systems (NSS) is an academic journal, published quarterly online and on paper, that has been created for publications of advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics etc. and their applications in any field.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Some articles in this issue: n-Refined Neutrosophic Modules, A Neutrosophic Approach to Digital Images, A Novel Method for Neutrosophic Assignment Problem by using Interval-Valued Trapezoidal Neutrosophic Number.

International Journal of Neutrosophic Science (IJNS) is a peer-review journal publishing high quality experimental and theoretical research in all areas of Neutrosophic and its Applications. Papers concern with neutrosophic logic and mathematical structures in the neutrosophic setting. Besides providing emphasis on topics like artificial intelligence, pattern recognition, image processing, robotics, decision making, data analysis, data mining, applications of neutrosophic mathematical theories contributions to economics, finance, management, industries, electronics, and communications are promoted.

[ADDRESSED CITATION] [HG211b] Henry Garrett, "Triangle-free search In Neutrosophic SuperHyperGraphs". Dr. Henry Garrett, 2024 (doi: 10.5281/zenodo.13512157). In this scientific research book, there are some scientific research chapters on "Extreme Vertex Cover In Neutrosophic SuperHyperGraphs" and "Neutrosophic Vertex Cover In Neutrosophic SuperHyperGraphs" about some scientific researches on Vertex Cover In Neutrosophic SuperHyperGraphs by two (Extreme/Neutrosophic) notions, namely, Extreme Vertex Cover In Neutrosophic SuperHyperGraphs and Neutrosophic Vertex Cover In Neutrosophic SuperHyperGraphs. With scientific research on the basic scientific research properties, the scientific research book starts to make Extreme Vertex Cover In Neutrosophic SuperHyperGraphs theory and Neutrosophic Vertex Cover In Neutrosophic SuperHyperGraphs theory more (Extremely/Neutrosophicly) understandable. Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in the following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4048 readers in Scribd. It"s titled "Beyond Neutrosophic Graphs" and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. [Ref] Henry Garrett, (2022). "Beyond Neutrosophic Graphs", Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 978-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in the following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 5046 readers in Scribd. It"s titled "Neutrosophic Duality" and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating In Neutrosophic SuperHyperGraphs in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It"s smart to consider a set but acting on its complement that what"s done in this research book which is popular in the terms of high readers in Scribd. [Ref] Henry Garrett, (2022). "Neutrosophic Duality", Florida: GLOBAL KNOW- LEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf).

International Journal of Neutrosophic Science (IJNS) is a peer-review journal publishing high quality experimental and theoretical research in all areas of Neutrosophic and its Applications. Papers concern with neutrosophic logic and mathematical structures in the neutrosophic setting. Besides providing emphasis on topics like artificial intelligence, pattern recognition, image processing, robotics, decision making, data analysis, data mining, applications of neutrosophic mathematical theories contributions to economics, finance, management, industries, electronics, and communications are promoted.