On the gracefulness of the graph P 2m,2n

Let $P_{a,b}$ denotes a graph obtained by identifying the endvertices of $b$ internally disjoint paths each of length $a.$Kathiresan conjectured that graph $P_{a,b}$ is graceful exceptwhen $a$ is odd and $bequiv 2$ (mod 4). In this paper we showthat the graph $P_{a,b}$ is graceful when both $a$ and $b$ areeven