Let  be a graph on p vertices with  where  is the minimum degree among the vertices of G. A  graph G is -cordial, if it is possible to label the edges of G with the numbers from the set  in such a way that at each vertex v, the sum modulo k of the labels on the edges incident with v satisfies the inequalities  and  for all  i, j, where  and  are, respectively, the number of vertices labelled with i and the number of edges labelled with j. In this paper, we define a new graph obtained by joining the central vertex of a wheel  to the end vertex of a path  by an edge e. We call this graph M-graph and is denoted by  We prove that for some values of m and n, the M-graph  is -cordial provided that k is odd. We also prove that when  the M-graph  is -cordial for all  and    is -cordial.

-cordial labelling, M-graph.