PAN Critical graphs). In this paper, we investigate the properties of these critical graphs. We also investigate the locally critical elements of graphs.

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Graph Coloring is one of the most popular topics in Graph Theory and Discrete Mathematics. In this paper, we review the various types of graph coloring concepts and the respective graph parameters defined and studied so far and discuss the significant results.

Let G(V, E) be a simple, finite and planar graph of order p and size q. In this paper, the concept of Fuzzy Quotient-3 Cordial Labeling was introduced. Let σ : V (G) → [0, 1] be a function defined by σ (v) = r 10 , r ∈ Z 4 − {0}. For each edge uv define µ : E(G) → [0, 1] by µ(uv) = 1 10 3σ (u) σ (v) where σ (u) ≤ σ (v). The function σ is called fuzzy quotient-3 cordial labeling of G if the number of vertices labeled with i and the number of vertices labeled with j differ by at most 1, the number of edges labeled with i and the number of edges labeled with j differ by at most 1 where i, j ∈ r 10 , r ∈ Z 4 − {0} , i = j. The number of vertices having label i denotes v σ (i) and the number of edges having label i denotes e µ (i). Here it is proved that the Star graph and Star related graphs are Fuzzy Quotient-3 Cordial.

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