Fuzzy Quotient‐3 Cordial Labeling of Some Trees of Diameter 5—Part III
P. Sumathi, S. Ramesh Kumar · 2021
Let G be a simple, finite, undirected, plannar and connected graph of order p and size q . Let |V|( G ) and E( G ) be the vertex set and edge set of the graph. Let σ :V( G ) → [0,1] be a function defined by σ ( ϑ )= γ /10, γ ϵ Z 4 -{10}. For each edge ωϑ , define μ : E( G ) → [0, 1] by μ ( ωϑ )= 1/10[3 σ ( ω )/ σ ( ϑ )] where σ ( ω ) ≤ σ ( ϑ ). Then σ is called fuzzy quotient-3 cordial labeling of G if for i ≠ jϵ { γ /10, γ ϵZ 4 -{0}}, v σ ( i ) and v σ ( j ) differ by at most 1 and e μ ( i) and e μ ( j ) differ by at most 1 where v σ ( i ) denotes the number of vertices mapped with the label i and e μ (i) denotes the number of edges mapped with the label. If graph G admits fuzzy quotient-3 cordial labelling then G is called fuzzy quotient-3 cordial graph. In this paper, the existence of fuzzy quotient-3 cordial labeling on some trees of diameter 5 denoted by ζ s 5 , 31 ≤ s ≤ 39 is investigated and the works are presented in this paper.