Liars dominationset on fuzzy graphs under join, corona, and lexicographic products

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.