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- H. G. Shekharappa, Shailaja S. Shirkol, Manjula C. Gudgeri
- 2013

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)

- Shailaja S. Shirkol, Manjula C. Gudgeri
- 2015

A signed Roman Dominating Function (SRDF) on a graph G is a function f : V(G) {-1, 1, 2} such that ∑ í µí²í µí²(í µí²í µí²) í µí²í 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)

- Shailaja S. Shirkol, Manjula C. Gudgeri
- 2013

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)

- H. B. Walikar, Shailaja S. Shirkol, Kishori P.Narayankar
- 2013

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)

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