Abstract. We introduce three types of extension of Gallai graph operator in to signed graphs-Gallai signed graph, product-Gallai signed graph and dot-Gallai signed graph. We find the forbidden subgraph characterizations of Gallai signed graph, product-Gallai signed graph and dot-Gallai signed graph.

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The graph G is said to be strongly regular with parameters (n, k, λ, µ) if the following conditions hold: (1) each vertex has k neighbours; (2) any two adjacent vertices of G have λ common neighbours; (3) any two non-adjacent vertices of G have µ common neighbours. In this paper we study two weaker notions of strongly regular graphs. A graph satisfying the conditions (1) and ( 2) is called an edge-regular graph with parameters (n, k, λ). We call a graph satisfying the conditions (1) and (3) a pseudo strongly regular graph with parameters