Liars Dominationset on fuzzy Graphs under Join, Corona, and Lexicographic Products
S.  Roseline Mary1, S. Ruban Raj2

1S. Roseline Mary, Department of Mathematics, Loyola College, Tiruvannamalai (Tamil Nadu), India.
2S. Ruban Raj, Department of Mathematics, RVS College of Arts and Science, Tiruchirappalli (Tamil Nadu), India.
Manuscript received on 25 July 2019 | Revised Manuscript received on 03 August 2019 | Manuscript Published on 10 August 2019 | PP: 1608-1610 | Volume-8 Issue-2S3 July 2019 | Retrieval Number: B12920782S319/2019©BEIESP | DOI: 10.35940/ijrte.B1292.0782S319
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Abstract: A set L⊆ V (G) of a fuzzy graphG = (V, E) is a liar’s dominating set if (1) for all υ∈ V (G), |N[υ] ∩ L | ≥ 2 and (2) for each pair ( u, v) ∈ V (G) of unmistakable vertices, |N[u] ∪ N[v] ∩ L| ≥ 3. In this paper, we consider the liar’s control number of some center graphs. Crown result of twofuzzy graphs which is undifferentiated from the idea crown item activity in fresh graph hypothesis is characterized. The level of an edge in crown result of fuzzy graphs is acquired. Additionally, the level of an edge in fuzzy graph framed by this activity as far as the level of edges in the given fuzzy graphs in some specific cases is found. In addition, it is demonstrated that crown result of two fuzzy graphs is compelling when two fuzzy graphs are powerful fuzzy graphs.
Keywords: Corona Product, Degree, Lexicographic, Fuzzy Graph.
Scope of the Article: Cryptography and Applied Mathematics