Let G be a simple, finite, connected, undirected, non-trivial graph with p vertices and q edges. V(G) be the vertex set and E(G) be the edge set of G. Let f:V(G)→{a,a+d,a+2d,a+3d,…,2(a+qd)} where a ≥0 and d≥1 is an injective function. If for each edge uv∈E(G) ,f^*:E(G)→{d,2d,3d,4d,…,qd} defined by f^* (uv)=|f(u)-f(v)| is a bijective function then the function f is called arithmetic sequential graceful labeling. The graph with arithmetic sequential graceful labeling is called arithmetic sequential graceful graph. Here we proved that swastik graph, path union of swastik graph, cycle of swastik graph is arithmetic sequential graceful graph.