Fuzzy Metric Dimension of Fuzzy Hypercube Qn and Fuzzy Boolean Graphs
M.Thusleem Furjana1, M.Bhanumathi2
1M.Thusleem furjana, Research Scholar, Department of mathematics, Government Arts college for Women (Autonomuos), Pudukkottai, affiliated to Bharathidasan University (Tiruchirappalli), Tamilnadu, India.
2M. Bhanumathi*, Principal (Retd.), Government Arts College for Women, Sivagangai, India.
Manuscript received on January 23, 2020. | Revised Manuscript received on February 05, 2020. | Manuscript published on February 30, 2020. | PP: 3690-3698 | Volume-9 Issue-3, February 2020. | Retrieval Number: C6226029320/2020©BEIESP | DOI: 10.35940/ijeat.C6226.029320
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Let G = (V, E, ) be a fuzzy graph. Let M be a subset of V. M is said to be a fuzzy metric basis of G if for every pair of vertices x, y V ‒ M , there exists a vertex w M such that d (w, x) d (w, y). The number of elements in M is said to be fuzzy metric dimension (FMD) of G and is denoted by (G). The elements in M are called as source vertices. In this paper, we study the fuzzy metric dimension of fuzzy hypercube Qn, fuuzy Boolean Graph BG2(G) and fuzzy Boolean Graph BG3(G).
Keywords: Fuzzy Boolean graph BG2(G), fuzzy Boolean graph BG3(G), fuzzy Hypercube Qn, fuzzy metric dimension.