  Let $G$ be a graph and $I=I(G)$ be its edge ideal. When $G$ is the clique sum
of two different length odd cycles joined at single vertex then we give an
explicit description of the symbolic powers of $I$ and compute the Waldschmidt
constant. When $G$ is complete graph then we describe the generators of the
symbolic powers of $I$ and compute the Waldschmidt constant and the resurgence
of $I$. Moreover for complete graph we prove that the Castelnuvo-Mumford
regularity of the symbolic powers and ordinary powers of the edge ideal
coincide.
