We give an exponential improvement to the lower bound on diagonal Ramsey numbers for any fixed number of colors greater than two.

We improve the lower bound on worst case trace reconstruction from ?(n5/4logn) to ?(n3/2log7n). As a consequence, we average ?(log9/4n loglogn) ?(log5/2n(loglogn)7).

In this paper, we obtain some upper and lower bounds for the general extended energy of a graph. As an application, we obtain few bounds for the (edge) Zagreb energy of a graph. Also, we deduce a relation between Zagreb energy and edge-Zagreb energy of a graph $G$ with minimum degree $delta ge2$. A lower and upper bound for the spectral radius of the edge-Zagreb matrix is obtained. Finally, we ...