Signed domination in Rooted product of a Path with a Cycle graph

Rashmi S B; Indrani Pramod Kelkar; Rajanna K R

doi:https://doi.org/10.14445/22315373/IJMTT-V58P508

International Journal of Mathematics Trends and Technology

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Volume 58 | Number 1 | Year 2018 | Article Id. IJMTT-V58P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V58P508

Signed domination in Rooted product of a Path with a Cycle graph

Rashmi S B, Indrani Pramod Kelkar , Rajanna K R

Abstract

A two valued function f defined on the vertices of a graph 𝐺 = (𝑉, 𝐸), 𝑓: 𝑉 → −1, 1 is a signed dominating function if the sum of its function values over any closed neighborhood of every vertex is at least 1, 𝑖. 𝑒. ∀𝑣 ∈ 𝑉, 𝑓(𝑁 𝑣 ) ≥ 1. The weight of a signed dominating function is 𝑤 𝑓 = 𝑓(𝑣) over all vertices 𝑣 ∈ 𝑉. The signed domination number of a graph G 𝛾𝑠 𝐺 is the minimum weight of a signed dominating function f on G. In this paper we present some results on signed dominating function of rooted product graph of a path with a cycle graph.

Keywords

Rooted product graph, Dominating function , Signed dominating function

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Citation :

Rashmi S B, Indrani Pramod Kelkar , Rajanna K R, "Signed domination in Rooted product of a Path with a Cycle graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 58, no. 1, pp. 62-65, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V58P508