Some Results on Super Mean Graphs
نویسندگان
چکیده
Let G be a graph and f : V (G) → {1, 2, 3, . . . , p+ q} be an injection. For each edge e = uv and an integer m ≥ 2, the induced Smarandachely edge m-labeling f∗ S is defined by f ∗ S(e) = ⌈ f(u) + f(v) m ⌉ . Then f is called a Smarandachely super m-mean labeling if f(V (G))∪ {f∗(e) : e ∈ E(G)} = {1, 2, 3, . . . , p+ q}. Particularly, in the case of m = 2, we know that f ∗(e) = f(u)+f(v) 2 if f(u) + f(v) is even; f(u)+f(v)+1 2 if f(u) + f(v) is odd. Such a labeling is usually called a super mean labeling. A graph that admits a Smarandachely super mean m-labeling is called Smarandachely super m-mean graph. In this paper, we prove that the H-graph, corona of a H-graph, G ⊙ S2 where G is a H-graph, the cycle C2n for n ≥ 3, corona of the cycle Cn for n ≥ 3, mCn-snake for m ≥ 1, n ≥ 3 and n 6= 4, the dragon Pn(Cm) for m ≥ 3 and m 6= 4 and Cm ×Pn for m = 3, 5 are super mean graphs, i.e., Smarandachely super 2-mean graphs.
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