aspg-24-1148-1791482518 20261008180158 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6430 2771-6449 2022 3 2 Sivasankar S Department of Mathematics, RV Institute of Technology and Management, Bangalore Said Broumi Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco The concepts of Neutrosophic secure edge domination number and neutrosophic total secure edge domination number in single valued neutrosophic graphs (SVNG) with strong arcs are introduced and analysed in this paper, and some of their properties are studied. The relationship between the neutrosophic secure edge dominance number style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif"; mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; mso-ansi-language:EN-IN'> style='mso-bidi-font-style:normal'> font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman";color:black;mso-ansi-language:EN-IN; mso-fareast-language:DE;mso-bidi-language:AR-SA'>γ style='mso-bidi-font-style:normal'> font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman";color:black;mso-ansi-language:EN-IN; mso-fareast-language:DE;mso-bidi-language:AR-SA'>nse style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif"; mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; mso-ansi-language:EN-IN'> style='mso-bidi-font-style:normal'> font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman";color:black;mso-ansi-language:EN-IN; mso-fareast-language:DE;mso-bidi-language:AR-SA'>G and its inverse style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif"; mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; mso-ansi-language:EN-IN'> style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif"; mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; mso-ansi-language:EN-IN;font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman";color:black;mso-ansi-language:EN-IN; mso-fareast-language:DE;mso-bidi-language:AR-SA'>γ style='mso-bidi-font-style:normal'> font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman";color:black;mso-ansi-language:EN-IN; mso-fareast-language:DE;mso-bidi-language:AR-SA'>-1 style='mso-bidi-font-style:normal'> font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman";color:black;mso-ansi-language:EN-IN; mso-fareast-language:DE;mso-bidi-language:AR-SA'>nse style='font-size:10.0pt;mso-ansi-font-size:10.0pt;font-family:"Cambria Math","serif"; mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; mso-ansi-language:EN-IN'> style='mso-bidi-font-style:normal'> font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman";color:black;mso-ansi-language:EN-IN; mso-fareast-language:DE;mso-bidi-language:AR-SA'>G is presented. The concepts inverse neutrosophic total edge domination set and inverse neutrosophic total edge domination number are also defined. Some of these concepts' properties are investigated. 2022 08 18 1148 https://creativecommons.org/licenses/by/4.0/ 10.54216/JNFS.030201 https://www.americaspg.com/journal/24/article/1148 https://www.americaspg.com/storage/8261.pdf