BOUNDS FOR THE EIGENVALUES OF GALLAI GRAPHS OF SOME GRAPHS.

The line graph L(G), of a graph G has the edges of G as its vertices and two distinct edges of G are adjacent in L(G), if they are adjacent in G. The Gallai graph (G) of a graph G, has the edges of G as its vertices and two distinct vertices are adjacent in (G) if they are adjacent edges in G, but do not lie on a triangle. The anti-Gallai graph κ(G) of a graph G has the edges of G as its vertices and two distinct edges of G are adjacent in κ(G), if they lie on a common triangle in G. In this paper we find bounds for the eigenvalues of Gallai graph of some class of graphs by using the adjacency spectrum of line graph and anti-Gallai graph. [ABSTRACT FROM AUTHOR]