Shailaja S. Shirkol

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Square lattice graphs L 2 (n) with the parameters (n 2 , 2 (n − 1) , n − 2, 2) are strongly regular and are unique for all n except n=4. however for n=4, we have two non-isomorphic strongly regular graphs. The non-lattice graph with parameters (16, 6, 2, 2) is known as Shrikhande graph. In this paper we show that every minimum total dominating set in(More)
In this paper we determine the number of minimum total dominating sets of paths and cycles and prove that the set of all minimum total dominating sets of a cycle forms a partially balanced incomplete block design. We also determine all cubic graphs on ten vertices in which the set of all minimum total dominating sets forms a Partially Balanced Incomplete(More)
Let G be a finite and simple graph with vertex set V (G), k ≥ 1 an integer and f (x) ≥ k for each v ∈ V (G), where N (v) is the open neighborhood of v, then f is a Smarandachely k-Signed total dominating function on G. A set {f1, f2,. .. , f d } of Smarandachely k-Signed total dominating function on G with the property that d i=1 fi(x) ≤ k for each x ∈ V(More)
A signed Roman Dominating Function (SRDF) on a graph G is a function f : V(G)  {-1, 1, 2} such that ∑ í µí²‡í µí²‡(í µí²–í µí²–) í µí²–í µí²–∈í µí±µí µí±µ|í µí±½í µí±½| ≥ í µí¿í µí¿ for every v Є V(G) and every vertex u Є V(G) for which f(u) =-1 is adjacent to at least one vertex w for which f(w) = 2. The weight of SRDF is the sum of its function values(More)
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