# Achromatic Coloring on Double Star Graph Families

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A Smarandachely k-constrained labeling of a graph G(V,E) is a bijective mapping f : V ? E ? {1, 2, .., |V| + |E|} with the additional conditions that |f(u) - f(v)| ? k whenever uv ? E, |f(u)-f(uv)| ? k and |f(uv)-f(vw)| ? k whenever u ? w, for an integer k ? 2. A graph G which admits a such...

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Given an arbitrary non-empty subset M of vertices in a graph G = (V,E), each vertex u in G is associated with the set fï¿½M(u) = {d(u, v) : v ? M, u ? v}, called its open M-distance-pattern. A graph G is called a Smarandachely uniform k-graph if there exist subsets M1,M2, ï¿½ï¿½ï¿½...

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A Smarandachely k-signed digraph (Smarandachely k-marked digraph) is an ordered pair S = (D, s) (S = (D, ï¿½)) where D = (V, A) is a digraph called underlying digraph of S and ï¿½ : A ? (e1, e2; ï¿½, ek) (ï¿½ : V ? (e1, e2, ï¿½, ek)) is a function, where each ei ? {+, -}....

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A Smarandachely k-signed graph (Smarandachely k-marked graph) is an ordered pair S = (G, s) (S = (G, ï¿½)) where G = (V, E) is a graph called underlying graph of S and s : E ? (e1, e2, ï¿½, ek) (ï¿½ : V ? (e1, e2, ï¿½, ek)) is a function, where each ei ? {+, -}. Particularly, a...

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No abstract available.

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A Smarandache drawing of a graph G is a drawing of G on the plane with minimal intersections for its each component and a circulant graph C(n; S) is the graph with vertex set V (C(n; S)) = {vi|0 ? i ? n-1} and edge set E(C(n; S)) = {vivj |0 = i ? j = n-1, (i-j)mod n e S}, S ? {1, 2, ï¿½ ,...