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Given graph G = (V, E), a dominating set S is a subset of vertex set V such that any vertex not in S is adjacent to at least one vertex in S. The domination number of a graph G is the minimum size of the dominating sets of G. In this paper we study some results on domination number, connected, independent, total and restrained domination number denoted by γ(G), γ c (G) ,γ i (G), γ t (G) and γ r (G) respectively in Jahangir graphs J 2,m .

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The closed neighborhood NG[v] of a vertex v in a graph G is the set consisting of v and of all neighborhood vertices of v. Let f be a function on V(G), the vertex set of G, into the set {-1, 1}. If ∑u∈N[v] f(u) ≤ 1 for all vertices v of G, then f is called a signed bad function of G. The maximum of the values of ∑v∈V(G) f(v), taking the maximum over all signed bad functions f of G, is called the signed bad number of G and denoted by β s (G). In this paper, we establish some upper bounds on the signed bad numbers for general graphs. In addition, we determine β s (G), when G is a complete graph, a cycle or a path.