Abstract
The Gallai graph Γ(G) of a graph G, has the edges of G as its vertices and two distinct vertices are adjacent in Γ(G) if they are adjacent edges in G, but do not lie on a triangle. In this paper we find the adjacency spectrum of Gallai graph of some graphs derived from simple graphs by certain operations, the characteristic polynomial for some graphs and exhibit the adjacency matrix of some other graphs.
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