Gallai-Type Theorems in Gallai Fuzzy Graphs on Domination Parameters

M. Kaliraja¹ , G. Karlmarx²

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.2 , pp.21-25, Apr-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.2125

Online published on Apr 30, 2019

Copyright © M. Kaliraja, G. Karlmarx . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
The Gallai fuzzy graph Γ(G) of a fuzzy graph G has the fuzzy edges of G as its fuzzy vertices and two distinct fuzzy edges of G are fuzzy incident in G, but do not span a fuzzy triangle in G. The Gallai fuzzy graphs are fuzzy spanning Gallai sub graphs of the well-known Class of fuzzy line graphs. Let γ(Γ(G)) and i(Γ(G)) denote the minimum fuzzy cardinality of a fuzzy dominating set of a Gallai fuzzy graph Γ(G)= (σ, μ) with n fuzzy vertices and maximum fuzzy degree Δ(Γ(G)), (Γ(G))≤ n-Δ(Γ(G), i(G) ≤ n-Δ(Γ(G)). In this manuscript, we characterized the fuzzy connected bipartite Gallai fuzzy graphs which achieve this upper bound. Here, we have shown that an arbitrary Gallai fuzzy Graph G are furnished with two conditions which are necessary if γ(Γ(G)) + Δ(Γ(G))= n and are sufficient to achieve n - 1 ≤ γ(Γ(G))+Δ(Γ(G)) ≤ n.

Key-Words / Index Term :
Gallai fuzzy graph, Gallai-type theorems, fuzzy domination parameters

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